1 00:00:00,920 --> 00:00:02,990 OK, good afternoon, everybody. Thank you for 2 00:00:02,990 --> 00:00:05,600 attending the second of our series, Serious, 3 00:00:06,020 --> 00:00:12,470 organized by Imperial University. And today it is 4 00:00:12,470 --> 00:00:17,090 my pleasure to introduce Dr. Pereira. She is our 5 00:00:17,090 --> 00:00:20,570 colleague in the part of mathematics. And I would 6 00:00:20,570 --> 00:00:23,210 like to mention that our seminar series is in 7 00:00:23,210 --> 00:00:27,500 collaboration with Florida A&M University. OK, so 8 00:00:27,590 --> 00:00:30,500 today I will present Dr. Berretta. I hope you can 9 00:00:30,500 --> 00:00:34,490 see the flyer and you can see the fire. Yes. Yes. 10 00:00:36,170 --> 00:00:38,840 Dr. Shibani Bharara is our colleague in the 11 00:00:38,840 --> 00:00:40,910 Department of Mathematics. And The Today Show will 12 00:00:40,910 --> 00:00:43,760 talk about the reduced multiplicative complexity, 13 00:00:43,760 --> 00:00:48,050 discrete, cosine, transform BCT circuitry. And I 14 00:00:48,050 --> 00:00:51,080 like to let you know that, in fact, Dr. Periera 15 00:00:51,410 --> 00:00:56,450 got her patent on this topic. This patent was 16 00:00:56,450 --> 00:01:00,550 awarded recently and she also has an NSF grant. OK, 17 00:01:00,980 --> 00:01:03,170 so if you are interested in the patent, is here 18 00:01:03,170 --> 00:01:05,780 with a patent number and then it's in the flier. 19 00:01:05,780 --> 00:01:08,060 So you can research that on your own, on your own. 20 00:01:08,570 --> 00:01:11,750 So at this point, I will stop share and then I 21 00:01:11,750 --> 00:01:14,720 will give the the Zoome, I should say, with the 22 00:01:14,720 --> 00:01:17,510 video, the controls I will give to Dr. Berretta. 23 00:01:20,450 --> 00:01:22,760 Thank you, Stefan, I appreciate the introduction 24 00:01:22,760 --> 00:01:28,670 and I appreciate you intuition to do this one. So 25 00:01:28,680 --> 00:01:28,880 good. 26 00:01:32,750 --> 00:01:36,140 Yes, but good afternoon, everyone. I'm going to 27 00:01:36,140 --> 00:01:39,260 talk about the reduced multiplicative complexity, 28 00:01:39,260 --> 00:01:43,680 discrete, cosine transform circuitry like the 29 00:01:44,120 --> 00:01:48,350 mentioned, this is based on the recent US patent. 30 00:01:50,760 --> 00:01:54,600 And what we going to discuss here? We have the we 31 00:01:54,600 --> 00:01:58,020 have the transforms that ICANN has formed, we have 32 00:01:58,590 --> 00:02:01,020 the well-known transform that we all know is 33 00:02:01,200 --> 00:02:04,290 discrete Fourier transform, if possible, to 34 00:02:04,290 --> 00:02:07,800 transform. That's the origin for that. The 50 is 35 00:02:07,800 --> 00:02:11,900 used to compute the discrete. Fourier transform 36 00:02:11,920 --> 00:02:14,290 and it's seamless efficiently. That was first 37 00:02:14,290 --> 00:02:18,550 arrived in 1965 as a result of work done by 38 00:02:18,940 --> 00:02:22,510 Coulier in Turkey. I mean, although Gauss has done 39 00:02:22,510 --> 00:02:27,320 some some work early on. So what we discuss 40 00:02:27,320 --> 00:02:29,990 discussing here, we have this head of input data, 41 00:02:29,990 --> 00:02:34,610 all the input signals, and then we propose self 42 00:02:34,610 --> 00:02:39,500 reconcile and Reddick's to discrete, cosine, 43 00:02:39,500 --> 00:02:43,160 transform technique to transform this set of data 44 00:02:43,160 --> 00:02:48,050 or the set of input into like an efficient 45 00:02:48,050 --> 00:02:51,530 computation. In a way, if I say that and how do we 46 00:02:51,530 --> 00:02:55,250 do it efficiently, we use the multiplication you 47 00:02:55,250 --> 00:02:58,670 accumulated accumulation unit so that we can cut 48 00:02:58,670 --> 00:03:02,000 down the complexity drastically so that we reduce 49 00:03:02,000 --> 00:03:06,620 the power consumption and a cheap area. So that's 50 00:03:06,620 --> 00:03:08,210 how I mean inclusion in here. 51 00:03:11,780 --> 00:03:16,850 Why it doesn't go down. OK, so if you think about 52 00:03:16,850 --> 00:03:20,060 it realistically, many problem in applied 53 00:03:20,060 --> 00:03:23,900 mathematics or the engineering cannot be solved by 54 00:03:23,900 --> 00:03:26,270 using the standard techniques. Why? When the 55 00:03:26,270 --> 00:03:30,140 problem or the U.S. or the data is getting bigger 56 00:03:30,140 --> 00:03:33,440 and bigger and bigger, the complexity of the 57 00:03:33,440 --> 00:03:37,190 problem will drastically increase the complexity 58 00:03:37,190 --> 00:03:40,760 increasing. Does this mean it requires longer time 59 00:03:40,940 --> 00:03:43,670 to execute these algorithms in a computer point of 60 00:03:43,670 --> 00:03:47,330 view? So what we could do is we could look at the 61 00:03:47,360 --> 00:03:50,690 structure. Fortunately, that's an advantage to 62 00:03:50,690 --> 00:03:56,270 design the fast algorithm. So why are we so 63 00:03:56,270 --> 00:03:58,100 fascinated with them? So they are the standard 64 00:03:58,100 --> 00:04:00,410 algorithm. If you we all know that in linear 65 00:04:00,410 --> 00:04:03,500 algebra point of view, Gaussian illumination is 66 00:04:03,500 --> 00:04:05,900 the standard algorithm. You can use that to solve 67 00:04:05,900 --> 00:04:08,330 a system of equation which is well known. In fact, 68 00:04:08,330 --> 00:04:11,540 the women still use the alien decomposition based 69 00:04:11,540 --> 00:04:14,750 on the Gulson elimination without using the 70 00:04:14,750 --> 00:04:17,540 structure explicitly. But if you could explore the 71 00:04:17,540 --> 00:04:20,360 structure, you can be very fast algorithm or in 72 00:04:20,360 --> 00:04:25,160 fact super fast algorithm. And then what we 73 00:04:25,160 --> 00:04:28,610 propose here is if you reduce the complexity that 74 00:04:28,610 --> 00:04:31,400 will reduce the power consumption and chip area 75 00:04:31,400 --> 00:04:34,680 drastically and that opens immense application in 76 00:04:34,700 --> 00:04:39,260 a digital signal processing lets you look at some 77 00:04:39,270 --> 00:04:42,890 structure defined matrices. So if you look at 78 00:04:42,890 --> 00:04:45,860 these Memphis's, you don't need any entries to 79 00:04:45,860 --> 00:04:49,610 determine for Matrix. You only need an operation 80 00:04:49,610 --> 00:04:51,860 to determine these. Minta says the first matrix 81 00:04:51,860 --> 00:04:55,190 that you see here is called the tablet. The second 82 00:04:55,190 --> 00:04:58,220 matrix that you see here is the Henckel. What are 83 00:04:58,220 --> 00:05:00,320 these murderousness, these matrices, upward 84 00:05:00,500 --> 00:05:03,650 movement type matrices. What you could do, you can 85 00:05:03,650 --> 00:05:07,250 define the movement based on the entries in these 86 00:05:07,580 --> 00:05:10,310 matrices. And then the first matrix, these 87 00:05:10,310 --> 00:05:12,650 bombings are associated with the red line and then 88 00:05:12,650 --> 00:05:15,680 the second matrix. You can even define the moments 89 00:05:16,010 --> 00:05:19,580 associated on the complex play. I mean, all the 90 00:05:19,580 --> 00:05:23,270 units that occur. And then the matrix that you see 91 00:05:23,270 --> 00:05:26,360 here, if you look at that matrix, is actually 92 00:05:26,360 --> 00:05:30,770 determined by the polynomial Frenchy. These 93 00:05:30,770 --> 00:05:34,610 polynomials can be used to construct this matrix 94 00:05:35,060 --> 00:05:39,260 recently, not that long ago, 2000, 2015, or 95 00:05:39,260 --> 00:05:43,010 something like that with my advisor, we derive a 96 00:05:43,010 --> 00:05:46,760 post algorithm while using this matrix, which we 97 00:05:46,760 --> 00:05:51,770 call a vision matrix. What we did was we compute 98 00:05:51,770 --> 00:05:54,200 the greatest combined device of the polynomial 99 00:05:54,200 --> 00:05:56,870 efficiently. If you come to the greatest common 100 00:05:56,870 --> 00:06:01,700 device of two polynomials that fill that need in 101 00:06:02,000 --> 00:06:05,150 cube operation. But what we did was instead of 102 00:06:05,150 --> 00:06:08,270 using in cube operation, we use in squared 103 00:06:08,270 --> 00:06:11,330 operation, which will drastically cut down the 104 00:06:11,330 --> 00:06:16,550 complexity due to the size of the system. So what 105 00:06:17,240 --> 00:06:20,450 we are, instead of using the vision, we also use 106 00:06:20,450 --> 00:06:23,780 another matrix which we call as a companion, which 107 00:06:23,780 --> 00:06:26,060 is associated with the polynomial division. We're 108 00:06:26,060 --> 00:06:27,850 going to talk about a little bit more in this 109 00:06:27,860 --> 00:06:31,700 tokarz. And then we use the displacement equations 110 00:06:31,700 --> 00:06:33,920 and then some operator. Then we go forward and 111 00:06:33,920 --> 00:06:37,190 backward between the polynomial and the Matrix 112 00:06:37,190 --> 00:06:41,030 language to prove that. And then whatever the 113 00:06:41,030 --> 00:06:43,850 matrix that you see top is called the squashy 114 00:06:43,850 --> 00:06:47,870 matrix. And then the bottom matrix is the tri 115 00:06:47,870 --> 00:06:51,320 diagonal matrix. Matrix is heavily using the 116 00:06:51,320 --> 00:06:54,110 polynomial interpolation when it comes to the 117 00:06:54,290 --> 00:06:57,830 rational function and in this triangular matrix 118 00:06:58,190 --> 00:07:01,100 can be used to solve a system of equation 119 00:07:01,100 --> 00:07:04,220 associated with the ionospheric simulation is 120 00:07:04,220 --> 00:07:06,950 beautiful. Once you come down and the thing will 121 00:07:06,950 --> 00:07:10,330 come down into nice, beautiful Azfar structure, 122 00:07:10,580 --> 00:07:13,160 then if you look at the characteristic polynomial 123 00:07:13,160 --> 00:07:16,370 of principles of matrix in here that satisfy the 124 00:07:16,370 --> 00:07:19,760 three terms for reconciliation, that relationship 125 00:07:19,760 --> 00:07:24,880 can be used to derive the first algorithm. This 126 00:07:24,880 --> 00:07:28,090 matrix, this is a special case of the tri diagonal 127 00:07:28,090 --> 00:07:30,690 and also unitary Herzenberg Matrix, unitary 128 00:07:30,700 --> 00:07:33,710 Heisenberg matrix, there's another family that guy 129 00:07:33,730 --> 00:07:38,830 can be used to analyze the enormous without 130 00:07:38,830 --> 00:07:42,550 orthogonal with respect to the unit circle. That 131 00:07:42,570 --> 00:07:46,120 assignment, one of the I mean, I think Cacio knows 132 00:07:46,120 --> 00:07:49,210 about him that time when he's one of the top 133 00:07:49,210 --> 00:07:53,630 mathematician in analysis and he has a lot of 134 00:07:53,630 --> 00:07:55,420 finesse, Afghan and everything, and he heavily 135 00:07:55,420 --> 00:08:00,070 wirrpanda. Watch this Herzenberg matrix. What is 136 00:08:00,070 --> 00:08:04,270 the nice thing about this one? This matrix? It has 137 00:08:04,270 --> 00:08:06,490 a structure. If you look at it, this matrix is 138 00:08:06,490 --> 00:08:10,390 fully determined only by using an operator. I mean, 139 00:08:10,630 --> 00:08:13,600 six parameters. You only need you need six 140 00:08:13,600 --> 00:08:17,650 parameters to determine this matrix. And then ABC 141 00:08:17,920 --> 00:08:21,550 Matrix is has SUNBERG or each one has them. But 142 00:08:22,090 --> 00:08:24,820 when we partition this matrix like this, like a 143 00:08:25,300 --> 00:08:29,350 partition, one, two, real Cathrine, when it is 144 00:08:29,350 --> 00:08:34,150 around one Miquel each one excuse me, each one 145 00:08:34,150 --> 00:08:37,360 positive burb when it is too it's, it's too close 146 00:08:37,510 --> 00:08:40,390 but in general it's key because it's simple. But 147 00:08:40,390 --> 00:08:43,750 and and we have to make sure that Matrix has to 148 00:08:43,750 --> 00:08:46,900 apply has a structure. We are all the entries 149 00:08:46,900 --> 00:08:50,590 below the fasullo was top dog zero. Look at this 150 00:08:50,590 --> 00:08:53,470 one. This has upward I mean upby has some 151 00:08:53,690 --> 00:08:57,000 structure and then if I partitioned into like that. 152 00:08:57,010 --> 00:08:59,950 So it's still the right one. One, two, hassira one. 153 00:09:00,310 --> 00:09:03,310 If I partition like that still one two blocks from 154 00:09:03,370 --> 00:09:06,640 one and I've got a single column so that has a 155 00:09:06,640 --> 00:09:09,310 round one. So what you could do when you have a 156 00:09:09,310 --> 00:09:12,700 structure matrix, when you have a huge system, if 157 00:09:12,700 --> 00:09:15,370 you could see the structure by using the 158 00:09:15,370 --> 00:09:18,280 generators, you can reduce the complexity 159 00:09:18,280 --> 00:09:21,700 drastically in a circuit interpretation or the 160 00:09:21,700 --> 00:09:24,640 chip design point of view. If you reduce the 161 00:09:24,640 --> 00:09:27,460 complexity drastically that when you are reducing 162 00:09:27,460 --> 00:09:30,580 the power consumption and also you are reducing 163 00:09:30,580 --> 00:09:35,020 the chip area and ultimately we can reduce the low 164 00:09:35,050 --> 00:09:39,310 cost chips. And then the matrix on the top is 165 00:09:39,310 --> 00:09:41,990 called amendment matrix. That's a polynomial 166 00:09:41,990 --> 00:09:45,430 random ornamentals. The baby version of that is 167 00:09:45,430 --> 00:09:49,420 the classical bannermen Imitrex, which we use to 168 00:09:49,420 --> 00:09:53,430 compute the polynomial and evolution efficiently. 169 00:09:53,470 --> 00:09:57,070 If you just use if you just try to evaluate the 170 00:09:57,070 --> 00:09:59,080 polynomial interpolation, if you have been given a 171 00:09:59,080 --> 00:10:01,630 set of indata, you're trying to construct the 172 00:10:01,630 --> 00:10:03,970 interpolation polynomial based on that. If you are 173 00:10:03,970 --> 00:10:07,290 try to do it is computational again, you it 174 00:10:07,330 --> 00:10:10,600 regarding cube operation. But if you could analyse 175 00:10:10,600 --> 00:10:13,660 the structure of the inputs that could cut down 176 00:10:13,660 --> 00:10:16,930 the complexity from and you do in squared 177 00:10:16,990 --> 00:10:19,300 operation. And if you could further explore 178 00:10:19,300 --> 00:10:21,730 through the displacement equation, which we 179 00:10:22,300 --> 00:10:26,230 actually define the operators, that could cut down 180 00:10:26,530 --> 00:10:30,040 more. So a structure simply defined many things 181 00:10:30,310 --> 00:10:33,970 and cut down the heavy computational burden 182 00:10:34,330 --> 00:10:37,450 drastically and then a matrix in the bottom. This 183 00:10:37,450 --> 00:10:40,930 is the discrete Fourier transform matrix, I put it 184 00:10:40,930 --> 00:10:43,270 one after the other. The reason for that is 185 00:10:43,630 --> 00:10:48,130 discrete. For the transform matrix can be seen as 186 00:10:48,130 --> 00:10:53,710 the random Animatrix, but the NRA, the Primedia 187 00:10:53,920 --> 00:10:57,730 groups of unity, the not seen here like here, see, 188 00:10:57,730 --> 00:11:01,030 you have a zero on one applauding minus one. These 189 00:11:01,030 --> 00:11:03,160 are the degrees zero degrees, one or two degrees 190 00:11:03,160 --> 00:11:07,630 and minus one polynomial x1 abraxane are the roots 191 00:11:07,630 --> 00:11:10,090 of the degree and polynomial. You simply what you 192 00:11:10,090 --> 00:11:12,460 do here is you simply go forward and backward 193 00:11:12,460 --> 00:11:16,180 between the polynomial language and the matrix 194 00:11:16,180 --> 00:11:20,710 language. And I mentioned earlier, DFT say a fifty 195 00:11:20,710 --> 00:11:26,590 algorithm first came to derive the algorithm for 196 00:11:26,590 --> 00:11:29,170 this BFE matrix that was in nineteen sixty four. 197 00:11:29,170 --> 00:11:34,150 All Logo's has done some work early on and and 198 00:11:34,180 --> 00:11:36,610 that first arrived in nineteen sixty five that 199 00:11:36,610 --> 00:11:40,210 arrived. What did they want. They want to analyze 200 00:11:40,210 --> 00:11:43,480 the rotation of the helium three molecule from 201 00:11:43,480 --> 00:11:47,050 then from that point till today, dramatically and 202 00:11:47,050 --> 00:11:52,260 significantly enroll in many areas including 203 00:11:52,450 --> 00:11:56,020 polynomial multiplication, matrix factorization 204 00:11:56,320 --> 00:12:01,990 and then solving a PD and then image compression, 205 00:12:01,990 --> 00:12:05,080 signal processing, barcode recognition and you 206 00:12:05,080 --> 00:12:06,430 name it, it's there. 207 00:12:08,770 --> 00:12:11,710 So what we talk here is what what is the 208 00:12:11,710 --> 00:12:15,910 fundamental basis? Well, my intuition pushed the 209 00:12:15,910 --> 00:12:21,730 reduction of circuit complexity is that it has 210 00:12:22,000 --> 00:12:27,100 been used in gypping. And IMPAC communities join 211 00:12:27,550 --> 00:12:30,760 photography expert group and then moving 212 00:12:30,940 --> 00:12:35,320 photography expert groups and then the DCP is the 213 00:12:35,470 --> 00:12:39,400 key or the or the I mean placeholder for the 214 00:12:39,400 --> 00:12:42,500 hearing, which is highly efficient with your code. 215 00:12:42,880 --> 00:12:46,270 So that's the centerpiece. So if you can solve a 216 00:12:46,270 --> 00:12:49,090 problem for interface, you'll simply solve a 217 00:12:49,090 --> 00:12:52,150 problem in many discipline. What I did through 218 00:12:52,150 --> 00:12:56,080 that, I designed the multiplayer accumulator units, 219 00:12:56,260 --> 00:12:59,920 the lowest that you could do, whereas you actually 220 00:12:59,920 --> 00:13:03,610 can construct the circuit for Real-Life 221 00:13:03,610 --> 00:13:06,010 implementation. I mean, you can put it in like 222 00:13:06,370 --> 00:13:09,340 wherever you can put it in a mobile phone, you can 223 00:13:09,340 --> 00:13:12,640 put it in a tablet or the laptop or the digital 224 00:13:12,640 --> 00:13:16,900 radios wherever you want to go. And then through 225 00:13:16,900 --> 00:13:20,260 the proper circuitry, we have a dedicated 226 00:13:20,260 --> 00:13:24,100 processing unit for that one and that goes as a 227 00:13:24,100 --> 00:13:28,290 module in there. So that's that's the beauty of it. 228 00:13:28,300 --> 00:13:31,810 And then we I mean, we talk a little bit more 229 00:13:31,810 --> 00:13:34,960 about it. And this is this is one of the figures 230 00:13:34,960 --> 00:13:38,050 in the patent. And then that I'm not going to 231 00:13:38,050 --> 00:13:42,850 teach the computer science, but this is this is 232 00:13:42,850 --> 00:13:46,150 what we are going to do. Let me talk a little bit 233 00:13:46,150 --> 00:13:48,790 about this one. So, I mean, here we have a process 234 00:13:48,820 --> 00:13:55,870 every which is our CPU or Shibu or whatever. Right. 235 00:13:55,870 --> 00:14:00,190 Or the cool. So the process of how this reduced 236 00:14:00,190 --> 00:14:03,340 multiplicative circuitry unique. So what we do is 237 00:14:03,400 --> 00:14:07,750 we put that unit as a module in Sebu or the GPU, 238 00:14:07,750 --> 00:14:10,090 and then these are connected to the memory. And 239 00:14:10,090 --> 00:14:13,370 then memory is the one we we carry on most bios 240 00:14:13,450 --> 00:14:16,600 like basically input output operations and then 241 00:14:16,600 --> 00:14:19,680 the mass storage. We have the hard drive and then 242 00:14:19,690 --> 00:14:23,230 the flash and then we have a transmitter. You need 243 00:14:23,620 --> 00:14:26,560 for the recursive information because we have one 244 00:14:26,560 --> 00:14:28,890 of them has to be around recursively for people 245 00:14:28,900 --> 00:14:33,500 that we have to include. Let me let me put this to 246 00:14:33,670 --> 00:14:36,280 show these what I'm talking about. So in there in 247 00:14:36,280 --> 00:14:40,150 this transmitter, in this unit, we have all the 248 00:14:40,450 --> 00:14:44,170 all the processing things that we wanted. Patiala, 249 00:14:44,170 --> 00:14:47,130 which which in this case is a recovery procedure. 250 00:14:47,380 --> 00:14:50,560 Carry on here and then this is through the bus 251 00:14:50,890 --> 00:14:54,160 link. But I mean, it's up to you, right. So 252 00:14:54,160 --> 00:14:58,420 whatever the whatever the link that you use, Bosso, 253 00:14:58,420 --> 00:15:00,970 the ring or the whatever the topology that you use, 254 00:15:00,970 --> 00:15:04,750 you use it. OK, then then we have a display unit 255 00:15:05,410 --> 00:15:08,890 typically, of course, in the Army information, we 256 00:15:08,890 --> 00:15:12,100 have a display unit and then we have the input 257 00:15:12,100 --> 00:15:15,160 devices. We know the input devices when it comes 258 00:15:15,160 --> 00:15:18,010 to the computer line, which all of us know. And 259 00:15:18,010 --> 00:15:21,280 then the navigation device, if you want to include, 260 00:15:21,280 --> 00:15:24,190 we include navigation device and then that one is 261 00:15:24,190 --> 00:15:26,730 directly connected to the module that we put it in 262 00:15:26,740 --> 00:15:31,120 that you view. And then we have sensors, GPS and 263 00:15:31,120 --> 00:15:33,610 everything can be connected to that through the 264 00:15:33,610 --> 00:15:37,360 bustling. And then we have the signals like extra 265 00:15:37,360 --> 00:15:40,300 like a speakers or whatever, like extra things. 266 00:15:40,900 --> 00:15:43,560 And then the output control in this one is like a 267 00:15:43,570 --> 00:15:47,770 USB, BS and then wired or wireless, whatever, 268 00:15:48,370 --> 00:15:50,500 whatever the network you are using. And we can 269 00:15:50,500 --> 00:15:53,380 install this one in the server or we can install 270 00:15:53,380 --> 00:15:56,850 this one in the server and a client in a booth. 271 00:15:56,890 --> 00:16:00,740 And so we put the module in the processing here 272 00:16:00,740 --> 00:16:05,550 and the network here, we have the network Ethernet 273 00:16:05,560 --> 00:16:09,340 or coaxial or phone, whatever the networking that 274 00:16:09,340 --> 00:16:12,640 you're going to use to that. This is the 275 00:16:12,640 --> 00:16:17,200 processing circuitry machine that we propose based 276 00:16:17,200 --> 00:16:22,600 on the reduction of complexity circuitry. And this 277 00:16:22,600 --> 00:16:25,060 is one of the figures, so I will add the end 278 00:16:25,300 --> 00:16:29,610 should have been. And then we'll go back to the 279 00:16:29,850 --> 00:16:35,190 transform again, so we have the food at TransWoman. 280 00:16:35,220 --> 00:16:38,370 This guy has subfamilies, despard, cosine 281 00:16:38,370 --> 00:16:41,970 transwoman descript sine transform. These guys are 282 00:16:41,970 --> 00:16:44,730 the real version of that discrete Fourier 283 00:16:44,730 --> 00:16:49,620 transform. It's always due to the issues in 284 00:16:50,040 --> 00:16:53,670 allocations and then extraction and then the data 285 00:16:53,670 --> 00:16:57,300 storage. It's always good to work with Urías 286 00:16:57,510 --> 00:17:00,050 rather than the complex, especially when when it 287 00:17:00,060 --> 00:17:04,080 comes to the pattern of processing. So in that 288 00:17:04,080 --> 00:17:08,160 case, that drives us to talk about the real 289 00:17:08,160 --> 00:17:10,830 version of this bigfooted transwoman. You can see 290 00:17:10,830 --> 00:17:12,810 that there are a bunch of version, one of the four 291 00:17:12,810 --> 00:17:16,770 here. I mean, there was one of before there. These 292 00:17:16,770 --> 00:17:19,470 are the main radians. But these variants goes up 293 00:17:19,470 --> 00:17:23,010 to eight versions. And these variants, based on 294 00:17:23,010 --> 00:17:25,320 the British play only one boundary conditions 295 00:17:25,320 --> 00:17:27,000 based on the boundary condition you have with 296 00:17:27,000 --> 00:17:30,930 different different matrices. Any I mean, I put 297 00:17:30,930 --> 00:17:33,060 this constructed version, but look at how 298 00:17:33,060 --> 00:17:36,690 cumbersome these are for a dense matrices. Right. 299 00:17:36,690 --> 00:17:39,300 And each of these this one is in plus one by and 300 00:17:39,300 --> 00:17:42,630 plus one. This is these guys, I imagine in minus 301 00:17:42,630 --> 00:17:46,290 one by minus one. These guys, I invite you in. And 302 00:17:46,290 --> 00:17:48,900 so as these guys. Right. And among these 303 00:17:48,900 --> 00:17:54,000 transformation DCT one was first appeared in 304 00:17:54,000 --> 00:17:59,760 nineteen eighty five and he's a man hunt and then 305 00:17:59,940 --> 00:18:04,050 DCG to NBC three or separate around nineteen 306 00:18:04,050 --> 00:18:08,100 seventy nine three three. Actually the electrical 307 00:18:08,100 --> 00:18:10,920 engineers or the electrical engineers are the one 308 00:18:10,920 --> 00:18:14,220 who proposed these transform DCG two and basically 309 00:18:14,230 --> 00:18:17,610 three was introduced by Ohama Nitrogen and Rowel. 310 00:18:18,180 --> 00:18:20,560 I mean it all passed out recently. I mean this, 311 00:18:20,970 --> 00:18:23,880 it's very sad. I mean he did tremendous work for 312 00:18:23,880 --> 00:18:25,890 the digital signal processing based on the 313 00:18:25,890 --> 00:18:28,940 discrete cosine frontwoman. His book is a very 314 00:18:28,950 --> 00:18:35,040 well and very famous anyway. So then BCT for DST, 315 00:18:35,040 --> 00:18:41,280 one end used for or was invented by AKG around 316 00:18:41,280 --> 00:18:45,390 like nineteen seventy five and then DSG two and 317 00:18:45,390 --> 00:18:50,580 BSD three wars. Did I mean introduced by Cakra and 318 00:18:50,580 --> 00:18:53,790 Salangi. All these are electrical engineers and 319 00:18:53,790 --> 00:18:57,360 they use these transform to reduce the complexity. 320 00:18:57,360 --> 00:19:01,620 But in 1994, Gilbert Shang, who was the 321 00:19:01,620 --> 00:19:05,360 mathematician anonymity, very famous. We always 322 00:19:05,370 --> 00:19:08,940 use his books when it comes to the limit. Anyway, 323 00:19:08,940 --> 00:19:13,320 he's the one who first shows that the columns of 324 00:19:13,680 --> 00:19:18,480 DCD one up to four are the eigenvectors with 325 00:19:18,480 --> 00:19:21,690 respect to the symmetric, with respect to the 326 00:19:21,690 --> 00:19:23,850 symmetric. Second different equation with this 327 00:19:23,870 --> 00:19:27,660 between the seven biodegradation for the DCG one 328 00:19:27,660 --> 00:19:32,700 up to four. Then later on I not writing at all, 329 00:19:32,700 --> 00:19:35,100 which has been around like a two thousand six. 330 00:19:35,430 --> 00:19:38,610 They used the same approach that was used by 331 00:19:38,610 --> 00:19:41,780 Gilbert Strang to show that the other transform 332 00:19:41,790 --> 00:19:45,570 which are DC to fire up to this eighty eight and 333 00:19:45,570 --> 00:19:50,610 Bisdee one up to the eight. The columns are the 334 00:19:50,610 --> 00:19:52,830 eigenvectors of symmetric seven different 335 00:19:52,830 --> 00:19:55,370 situation with respect to the Dirichlet only one 336 00:19:55,600 --> 00:19:59,670 recognition that orthogonality is needed because 337 00:19:59,670 --> 00:20:03,630 if you remember Havok high efficiency geocoding is 338 00:20:03,630 --> 00:20:07,470 that they say they need the suboptimal bit how 339 00:20:07,470 --> 00:20:09,810 they get this hubo optimality through the 340 00:20:09,810 --> 00:20:12,900 orthogonality. So the orthogonality is important. 341 00:20:13,500 --> 00:20:16,620 When you think about the transform point of view, 342 00:20:16,950 --> 00:20:21,390 these are some, these are very few, but quite non, 343 00:20:21,660 --> 00:20:28,520 non, non algorithm in the DFT and Vesty. This is a 344 00:20:28,530 --> 00:20:32,640 change. Smith and Frank and this is also Eskin, 345 00:20:32,640 --> 00:20:35,480 his son, and this is the only paper that no one 346 00:20:35,520 --> 00:20:39,210 shows the road with his son and his son said, OK, 347 00:20:39,210 --> 00:20:41,700 I don't want to write anymore. His son was in MIT 348 00:20:41,940 --> 00:20:45,300 and he has to be in electrical engineering and 349 00:20:45,300 --> 00:20:48,030 also in math. So he said, I don't want to be 350 00:20:48,030 --> 00:20:51,120 writing paper with your father. So because people 351 00:20:51,120 --> 00:20:53,280 doesn't know who wrote it. So I don't want it to 352 00:20:53,280 --> 00:20:56,480 ruin my career. So that's only paper that he wrote 353 00:20:56,490 --> 00:21:00,090 with his father, which was my advice anyway. So he 354 00:21:00,090 --> 00:21:03,690 was going to Stanford. So that's their paper. 355 00:21:03,690 --> 00:21:06,000 Their paper is beautiful. It's a completely 356 00:21:06,000 --> 00:21:10,590 different level of thinking of this industry. And 357 00:21:10,590 --> 00:21:13,170 then they actually have NSF grant based on they 358 00:21:13,170 --> 00:21:18,150 actually had NSF ground based on that paper. And 359 00:21:18,150 --> 00:21:22,240 this is a long shot. They are working. DCD seems 360 00:21:22,260 --> 00:21:25,730 quite a long time. And this was strength. Yeah. 361 00:21:25,740 --> 00:21:29,120 Bowstring again. This is a Valdimir, you banro 362 00:21:29,870 --> 00:21:32,450 famous electrical engineers, they work with those 363 00:21:33,020 --> 00:21:36,260 and this is with my advice and myself and this is 364 00:21:36,260 --> 00:21:40,580 myself and this is with me and my collaborator 365 00:21:40,580 --> 00:21:45,500 general in the department. So these are I mean, 366 00:21:45,500 --> 00:21:48,620 even though this I'm not that happy. I mean, to be 367 00:21:48,620 --> 00:21:52,580 honest. I mean, I can tell you the truth. The 368 00:21:52,580 --> 00:21:57,070 reason is those are similar to what is in here. 369 00:21:57,440 --> 00:22:00,140 The only difference that I, I reduce the 370 00:22:00,140 --> 00:22:02,960 complexity again. But it's not like a dramatic 371 00:22:03,110 --> 00:22:05,870 reduction, like we are talking in here so that we 372 00:22:05,870 --> 00:22:09,260 can actually pick need or something that we could 373 00:22:09,260 --> 00:22:15,470 do out of it. Right. So what I did here so in here 374 00:22:15,470 --> 00:22:18,710 are you will only see the factorization, but the 375 00:22:18,710 --> 00:22:22,040 underlying complexity is not here. And I'm not 376 00:22:22,040 --> 00:22:24,970 going to show the proof in here, but I will tell 377 00:22:25,250 --> 00:22:29,750 how it was derived. So we have these crosswell 378 00:22:29,780 --> 00:22:32,180 metrics, like I said, all of these versions of 379 00:22:32,180 --> 00:22:35,990 there. So these transformed matrix can be 380 00:22:35,990 --> 00:22:39,830 represented based on the I mean, if you take the 381 00:22:39,830 --> 00:22:42,470 characters polynomial of these matrices based on 382 00:22:42,470 --> 00:22:45,260 those characteristic polynomial, we can construct 383 00:22:45,260 --> 00:22:47,720 the chip polynomial in a plus kind of the 384 00:22:47,720 --> 00:22:50,570 traditional polynomial in the second guy. These 385 00:22:50,570 --> 00:22:53,870 polynomial satisfy that a constellation. So what 386 00:22:53,870 --> 00:22:58,190 we do I mean, what my advice office did was the 387 00:22:58,190 --> 00:23:02,410 one that he got NSF anyway, so he had the Vandeman 388 00:23:02,410 --> 00:23:04,910 The Matrix. Right. Associated with the chip 389 00:23:05,160 --> 00:23:07,120 polynomial in the first kind of the Tchividjian 390 00:23:07,460 --> 00:23:10,730 meaning the second. He took that matrix like huge, 391 00:23:10,730 --> 00:23:16,910 cumbersome, dense matrix and he proposed the sale 392 00:23:16,910 --> 00:23:20,180 of goods you algorithm for the random order matrix. 393 00:23:20,810 --> 00:23:24,320 And that was very neat and nice and beautiful. And 394 00:23:24,320 --> 00:23:26,900 how did you propose that he proposed through 395 00:23:27,410 --> 00:23:30,440 through the introduction of a polynomial division 396 00:23:30,590 --> 00:23:33,260 in the Matrix language. So you had to go forward 397 00:23:33,260 --> 00:23:35,660 and backward between the polynomial division and 398 00:23:36,500 --> 00:23:39,710 Matrix. I mean, what's then matrix representation 399 00:23:39,710 --> 00:23:43,370 techni? So it's beautiful and elegant anyway, then 400 00:23:43,850 --> 00:23:48,770 later on or before? I think early on with his 401 00:23:48,770 --> 00:23:53,360 advisor, Kailath, he's he's also electrical 402 00:23:53,360 --> 00:23:57,740 engineer, very famous guy, Stanford guy. So with 403 00:23:57,740 --> 00:24:02,030 him, he worked on these again, these 404 00:24:02,030 --> 00:24:04,880 transformations. And he said this transformation, 405 00:24:04,880 --> 00:24:07,730 the corresponding transformation matrices can be 406 00:24:07,730 --> 00:24:10,760 written as a product of random Animatrix times the 407 00:24:10,760 --> 00:24:14,700 way the words we can like I mean, like same with 408 00:24:14,720 --> 00:24:17,630 Matrix that we have in a DFT, which are the ones 409 00:24:17,630 --> 00:24:19,400 that are associated with the twin. In fact, as 410 00:24:19,430 --> 00:24:22,040 these two fact, we can change so that the 411 00:24:22,040 --> 00:24:27,200 complexity can change based on that enemy. So one 412 00:24:27,210 --> 00:24:30,470 sees that. So then he he himself devised these 413 00:24:30,710 --> 00:24:33,410 distribution polynomial corresponding to the E 414 00:24:33,410 --> 00:24:37,760 transform can can be derived through the recording 415 00:24:37,790 --> 00:24:41,780 process. And also you can propose the self 416 00:24:41,780 --> 00:24:44,810 recursive process for the random order matrix 417 00:24:44,810 --> 00:24:47,940 associated with the chip. OK, he did that and with 418 00:24:47,990 --> 00:24:51,620 this he did that. OK, so let me try to combine 419 00:24:51,620 --> 00:24:53,900 them. So I was thinking, OK, let me try to combine 420 00:24:53,900 --> 00:24:56,450 them. But he in fact could give you the lowest 421 00:24:56,450 --> 00:24:59,360 complexity because he didn't look explicitly on 422 00:24:59,360 --> 00:25:02,390 BCT algorithms. He work on the Vandeman. I guess 423 00:25:02,420 --> 00:25:05,510 that's what he's interested anyway. So and then 424 00:25:05,510 --> 00:25:08,180 the Kailath and also the thing that they talk 425 00:25:08,180 --> 00:25:11,780 about discrete transform and then they talk about 426 00:25:11,780 --> 00:25:13,640 the renderman of interest. They also talk about 427 00:25:13,640 --> 00:25:16,100 the weights, how they are related or the nodes 428 00:25:16,340 --> 00:25:19,270 corresponding to the degree employment. I mean a 429 00:25:19,280 --> 00:25:23,150 degree in Chibbaro like polynomials. And then it's 430 00:25:23,150 --> 00:25:25,730 not explicit. Paloma's writes. Right, like what it 431 00:25:25,730 --> 00:25:29,640 all means anyway. So then what we could do is, OK, 432 00:25:29,700 --> 00:25:32,210 now we can convert this, OK, if he has his own 433 00:25:32,210 --> 00:25:34,370 formula for the RenderMan matrix, the other people 434 00:25:34,370 --> 00:25:37,670 has his own formula for the management and that we 435 00:25:38,030 --> 00:25:40,910 saw what I say, OK, if that is the case, we have 436 00:25:40,910 --> 00:25:43,790 the weights, we have the random order. Okay, so we 437 00:25:43,790 --> 00:25:47,220 combine them together. How we do that. OK, I need 438 00:25:47,220 --> 00:25:51,530 the I need to define the polynomial division on 439 00:25:51,530 --> 00:25:54,080 the matrix form again because my transformation is 440 00:25:54,080 --> 00:25:57,010 different. It's like a hybrid of those guys. OK, 441 00:25:57,140 --> 00:26:00,200 so then I define the polynomial division in the 442 00:26:00,200 --> 00:26:04,310 Matrix school and then I extract those portion and 443 00:26:04,310 --> 00:26:07,430 remained as the matrix. For once we have the 444 00:26:07,430 --> 00:26:10,290 matrix form. We can convert into the polynomial. 445 00:26:10,290 --> 00:26:13,340 For once we have the polynomial, we have the N 446 00:26:13,340 --> 00:26:17,270 right, which are order which can be used. So take 447 00:26:17,270 --> 00:26:21,680 those, take those nodes and took this as a zero of 448 00:26:21,680 --> 00:26:24,890 the degree in polynomial. And then I use to divide 449 00:26:24,890 --> 00:26:27,870 and conquer technique to reduce the. Divide and 450 00:26:27,870 --> 00:26:30,630 conquer technique, every step like you reduce the 451 00:26:30,630 --> 00:26:33,330 big divide to enable us to innovate, we know what 452 00:26:33,330 --> 00:26:35,760 we're doing to the point of always trying to look 453 00:26:36,000 --> 00:26:39,090 at something like that. Right. And then there are 454 00:26:39,090 --> 00:26:42,370 some trigonometric proofing side here and there. 455 00:26:42,690 --> 00:26:48,090 So this huge dense matrix can be represented in 456 00:26:48,090 --> 00:26:50,880 terms of the product of software that says this 457 00:26:50,880 --> 00:26:54,360 guy is the anti diagonal. I see like ones and 458 00:26:54,360 --> 00:26:57,630 zeros doesn't contribute for the multiplication of 459 00:26:57,630 --> 00:27:00,030 complexity at all because it's multiplication by 460 00:27:00,030 --> 00:27:04,380 one is not counted. And then these are identity 461 00:27:04,380 --> 00:27:07,830 matrices. Simply, this guy is a huge matrix with 462 00:27:07,830 --> 00:27:10,680 double reed and this is a diagonal matrix. This 463 00:27:10,680 --> 00:27:12,810 guy already wants this and contribute for the 464 00:27:12,810 --> 00:27:16,740 multiplication. That's beautiful. This guy is the 465 00:27:16,950 --> 00:27:21,510 diagonal guy but is only in number two and these 466 00:27:21,510 --> 00:27:23,850 guys are by diagonal. We only think about this one 467 00:27:23,850 --> 00:27:27,570 for the amount of complexity. And then these guys 468 00:27:27,570 --> 00:27:29,700 I want this is a permutation, beautiful 469 00:27:29,700 --> 00:27:32,130 punctuation day. This guy's identity, this is half 470 00:27:32,130 --> 00:27:35,760 of that. But you don't have to start within, say, 471 00:27:35,760 --> 00:27:38,220 when you start with n you go to in order to win 472 00:27:38,220 --> 00:27:41,280 over two, then you go to Inovio for. I know before 473 00:27:41,400 --> 00:27:44,970 in 04 I know of. So ultimately, once you built the 474 00:27:44,970 --> 00:27:49,020 whole tree, you do the bottom up approach, you 475 00:27:49,020 --> 00:27:53,130 only compute the tool by two mattresses and then 476 00:27:53,130 --> 00:27:56,610 from there you build up to construct the whole 477 00:27:56,760 --> 00:27:59,820 matrix and now you're also able to pull some nice, 478 00:27:59,820 --> 00:28:01,860 beautiful results, the outstanding results 479 00:28:01,860 --> 00:28:06,700 combining these two NBC defore in the literature. 480 00:28:06,720 --> 00:28:09,840 And from that, that's the other reason of that 481 00:28:09,840 --> 00:28:13,800 technicality is important. From this, I was able 482 00:28:13,800 --> 00:28:18,680 to connect all the results from DCG to an addict 483 00:28:18,810 --> 00:28:23,190 for which is around 1970 till till the till the 484 00:28:23,190 --> 00:28:26,010 publication of whatever this PEADEN So it's like 485 00:28:26,010 --> 00:28:29,340 nice. I simply I made a bridge to connect the 486 00:28:29,340 --> 00:28:32,670 existing factorization with the new representation 487 00:28:32,670 --> 00:28:34,900 so that you can go forward and backward between 488 00:28:34,900 --> 00:28:37,140 them because they they to go algorithm them, 489 00:28:37,410 --> 00:28:39,510 whatever the way that you want. If you wanted to 490 00:28:39,520 --> 00:28:42,750 compute one in terms of the other or if you have 491 00:28:42,750 --> 00:28:45,840 more memory or more storage, you use it, that's 492 00:28:45,840 --> 00:28:48,240 fine. You go to other transformation and you get 493 00:28:48,240 --> 00:28:52,440 the space from there. Or if you don't, how space 494 00:28:52,440 --> 00:28:54,420 or the memory. If you are concerned about the 495 00:28:54,420 --> 00:28:57,120 complexity, you could just use the proposed one. 496 00:28:57,300 --> 00:29:00,390 That's fine, too. So you have the nice bridge that 497 00:29:00,390 --> 00:29:02,640 connects in that this is the one that connecting 498 00:29:02,640 --> 00:29:06,240 the bridge. I mean, I don't have any proof in here, 499 00:29:06,690 --> 00:29:11,240 but I was showing some of the paper. So this one 500 00:29:11,240 --> 00:29:13,440 is once you divide them and this one is a piece of 501 00:29:13,440 --> 00:29:16,220 cake, to be honest. So it's just a principle of 502 00:29:16,220 --> 00:29:18,950 that one. So the other the first process is the 503 00:29:18,950 --> 00:29:21,020 cumbersome. And so as the second process, this is 504 00:29:21,020 --> 00:29:23,840 a piece of cake and this one is a little bit, but 505 00:29:23,840 --> 00:29:26,450 it's not that bad. I mean, it's not that bad, to 506 00:29:26,450 --> 00:29:29,690 be honest. And then because of this one, I was 507 00:29:29,690 --> 00:29:33,650 able to connect all the DCT three, which is the 508 00:29:33,650 --> 00:29:37,550 inverse of the two. That's the one that important 509 00:29:37,850 --> 00:29:40,910 for the beginning, because you remember I 510 00:29:40,910 --> 00:29:44,600 mentioned that for the big and big communities, 511 00:29:44,600 --> 00:29:48,760 they only use the optimal like a suboptimal 512 00:29:48,800 --> 00:29:52,730 transform mess that DCG to NDB three. So those are 513 00:29:52,730 --> 00:29:55,160 the important ones. So that's why these are 514 00:29:55,160 --> 00:29:58,640 considered in here. So then this one was like I 515 00:29:58,640 --> 00:30:03,170 mentioned, this is 23, which is Amina Dragonite 516 00:30:03,170 --> 00:30:06,140 Alwi nineteen seventy nine, so nineteen seventy 517 00:30:06,140 --> 00:30:09,940 nine till the day that we worked on this one. So 518 00:30:10,100 --> 00:30:12,440 look at the whole thing algorithm. You don't need 519 00:30:12,440 --> 00:30:14,900 pages and pages to write this and you will see a 520 00:30:14,900 --> 00:30:18,010 lot of memory and you will see a lot of storage. 521 00:30:18,500 --> 00:30:21,320 You don't need tons of quotes for that. And the 522 00:30:21,320 --> 00:30:24,530 beauty, look at the building. He did this part and 523 00:30:24,530 --> 00:30:27,440 that part can be computed parallel if you have 524 00:30:27,440 --> 00:30:29,450 about a process. No, the trend is better, a 525 00:30:29,450 --> 00:30:31,820 processing machine, learning algorithm, whatever 526 00:30:31,820 --> 00:30:34,260 that is that you're going to use. So this part 527 00:30:34,280 --> 00:30:36,740 does not depend on that part because this part 528 00:30:36,860 --> 00:30:41,120 depends. Only the victims zero up to a.. In order 529 00:30:41,120 --> 00:30:45,470 to minus one. In order to minus one. In order to 530 00:30:46,100 --> 00:30:48,950 see in one you they know what to like half of the 531 00:30:49,160 --> 00:30:52,190 matrix. So that one and this process can run 532 00:30:52,190 --> 00:30:55,760 through the parallel once to run the parallel. So 533 00:30:55,760 --> 00:30:58,230 not only that, we propose the was complex 534 00:30:58,240 --> 00:31:01,580 complexity that can also go down more. So that's a 535 00:31:01,580 --> 00:31:03,830 beauty need. You can run through it, if you will, 536 00:31:03,830 --> 00:31:06,380 or you can run with a parallel. You can combine 537 00:31:06,380 --> 00:31:10,670 those if they do in parallel algorithm one after 538 00:31:10,670 --> 00:31:15,410 the other. This is for the cosine three type. And 539 00:31:15,410 --> 00:31:17,630 then see, look at it again. I can run this 540 00:31:17,630 --> 00:31:21,920 algorithm and then I can cut down complexity more 541 00:31:21,950 --> 00:31:25,430 then I propose in this paper. And so you can see 542 00:31:25,430 --> 00:31:27,500 very clearly remember the discussion, Creevey, 543 00:31:27,500 --> 00:31:29,510 talk about the decision for you when it comes to 544 00:31:29,510 --> 00:31:33,200 the discrete Fourier transform when we want to be 545 00:31:33,370 --> 00:31:36,540 a 50 phosphoric transform algorithm. Every time 546 00:31:36,540 --> 00:31:38,420 when you have a fast food, you transform, you have 547 00:31:38,420 --> 00:31:41,060 a problem of size, and then you go like, I know 548 00:31:41,060 --> 00:31:42,860 what to do and what to do in order to. That's a 549 00:31:42,860 --> 00:31:46,010 decision three beautiful binary tree that we have 550 00:31:46,190 --> 00:31:50,210 the cost of computing this stages in this one is I 551 00:31:50,210 --> 00:31:53,330 know what we know. Two is cost is in. This is 552 00:31:53,330 --> 00:31:56,900 again in if I run the algorithm forty times, the 553 00:31:56,900 --> 00:32:01,190 total cost is eight times. But TI is the low base 554 00:32:01,190 --> 00:32:05,360 to win. But see, now that we have the pattern 555 00:32:05,420 --> 00:32:07,950 processes, right, if I have a parallel process for 556 00:32:07,970 --> 00:32:12,110 how people processes, this complexity will cut 557 00:32:12,110 --> 00:32:17,300 down in no p log base to a new WAPI, which is 558 00:32:17,300 --> 00:32:20,840 drastic when we how many patta processes because 559 00:32:20,840 --> 00:32:23,480 one does not depend on the other. I can run those 560 00:32:23,480 --> 00:32:26,900 things beautifully in a matter of process. And so 561 00:32:26,900 --> 00:32:30,200 it will reduce the circuit complexity and a power 562 00:32:30,200 --> 00:32:35,800 consumption and chip area again. So I can run this 563 00:32:35,800 --> 00:32:38,570 one as well, which is seamless. I said that BCT 564 00:32:38,630 --> 00:32:42,220 two and three one is the use of the other. Those 565 00:32:42,220 --> 00:32:46,450 are the ones or we consider a suboptimal transform 566 00:32:46,450 --> 00:32:49,780 for the highly efficient radial coding community 567 00:32:50,050 --> 00:32:54,370 or the joint expert group or the moving expert 568 00:32:54,370 --> 00:32:57,790 group. So that's what we have here. And then see 569 00:32:57,790 --> 00:33:00,850 how how nice, beautiful, simple this number of 570 00:33:00,850 --> 00:33:04,390 modifications and number of additions. I don't 571 00:33:04,390 --> 00:33:06,760 have a proof in here again. So how did I prove 572 00:33:06,760 --> 00:33:09,310 this to prove this one as a mathematician, we are 573 00:33:09,430 --> 00:33:13,780 interested about proof anyway. And so what we did 574 00:33:13,780 --> 00:33:16,720 was look at the ones high-octane this past 575 00:33:16,730 --> 00:33:19,240 mechanization. So I wanted to compute the 576 00:33:21,310 --> 00:33:24,760 these transform to the proposed factorization. So 577 00:33:24,760 --> 00:33:27,130 then I look at the complexity of this one 578 00:33:27,490 --> 00:33:29,890 depending on let me go back. Complexity of this 579 00:33:29,890 --> 00:33:32,740 task will depend on complexity and compute in this 580 00:33:32,740 --> 00:33:35,740 one. Complexity in computing. That one, that one, 581 00:33:35,890 --> 00:33:39,270 that one that this guy permutation is like in 582 00:33:39,300 --> 00:33:41,620 engineering point of the permutation is you take 583 00:33:41,620 --> 00:33:43,570 out all the wires and you put it in different 584 00:33:43,570 --> 00:33:45,700 order. That's a permutation. That's what four 585 00:33:45,700 --> 00:33:48,640 engineers point of view. So it's it's not it's not 586 00:33:49,390 --> 00:33:51,550 it's not expensive. Plus, if you take out those 587 00:33:51,550 --> 00:33:54,480 and put it in a sad note, that's implementation. 588 00:33:54,820 --> 00:33:58,420 OK, so the VITAC in this case, that's nice. 589 00:33:58,420 --> 00:34:01,420 Beautiful. And then I had one once. I mean, you 590 00:34:01,420 --> 00:34:04,060 remember when we according to the Rifkin's and 591 00:34:04,060 --> 00:34:08,410 then charge a loan when you when you multiply 592 00:34:08,410 --> 00:34:10,630 numbers or when you add numbers, you have to 593 00:34:10,630 --> 00:34:13,450 consider the floatplane operation. Right. Because 594 00:34:13,450 --> 00:34:16,140 it always come floating point operations of six 595 00:34:16,150 --> 00:34:21,370 times YTD X dynamite exchange Y times one plus 596 00:34:21,370 --> 00:34:25,600 Delta Delta is dependent on the machine position 597 00:34:25,600 --> 00:34:28,180 or the machine and so on. So you have to be 598 00:34:28,180 --> 00:34:31,540 careful when you multiply the numbers or when you 599 00:34:31,540 --> 00:34:34,060 add the numbers or if you multiply numbers one 600 00:34:34,060 --> 00:34:37,120 after the other, you are accumulating so many 601 00:34:37,120 --> 00:34:40,360 machine. I mean machine epsilon constants. So more 602 00:34:40,360 --> 00:34:43,480 you accumulate more. You have to worry about the 603 00:34:43,480 --> 00:34:46,660 number of decimal places which the algorithm is 604 00:34:46,660 --> 00:34:50,770 accurate up to anyway. So then this one see I have 605 00:34:50,830 --> 00:34:52,990 this radical effect. I don't like to keep it. So I 606 00:34:52,990 --> 00:34:55,390 was like, OK, let me pull it and then I'm going to 607 00:34:55,390 --> 00:34:57,970 put it at the end of the computation. So it will 608 00:34:58,270 --> 00:35:01,300 up to. And so then I only need the multiplier over 609 00:35:01,300 --> 00:35:03,600 there. I don't need like a multiplying in every 610 00:35:03,610 --> 00:35:06,490 state. So I put the multiply at the end rather 611 00:35:06,490 --> 00:35:09,670 than put in a multiply everywhere, every drop. And 612 00:35:09,670 --> 00:35:13,210 then in here only the cost contribute for this one 613 00:35:13,300 --> 00:35:16,690 I for this one I need multiply this, I need a 614 00:35:16,690 --> 00:35:19,600 multiplier. And then there's one cost of computing. 615 00:35:19,600 --> 00:35:23,770 This algorithm depend on twice the cost of 616 00:35:23,770 --> 00:35:27,610 computing, half of it. S and the cost of computing. 617 00:35:27,610 --> 00:35:31,660 This, that and this one I have that. I ended up 618 00:35:31,660 --> 00:35:34,630 with the first order difference he mentioned once 619 00:35:34,630 --> 00:35:37,180 I had the first order difference equation I solved 620 00:35:37,180 --> 00:35:40,570 with respect to the initial condition. And then 621 00:35:40,570 --> 00:35:44,020 that will help me to divide these complexity that 622 00:35:44,020 --> 00:35:46,630 we mentioned here. And this is the number of 623 00:35:46,630 --> 00:35:48,790 additions, number of additions in electrical 624 00:35:48,790 --> 00:35:51,920 engineering point of view. They represent as ediz 625 00:35:51,950 --> 00:35:54,390 edges are very cheap, like a one to two to like 626 00:35:54,490 --> 00:35:57,280 maximum five dollars. That's not bad. Multiplex's 627 00:35:57,290 --> 00:35:59,200 either one very expensive. So Multiplex's 628 00:35:59,200 --> 00:36:03,430 sometimes cost ten thousand dollars. So movie 629 00:36:03,430 --> 00:36:05,440 costs the Multiplex's more. We reduce the 630 00:36:05,440 --> 00:36:09,310 Multiplex's more, we save the money or the how we 631 00:36:09,310 --> 00:36:12,490 design the circuits. So this is the most of that 632 00:36:12,490 --> 00:36:15,850 one which is again and what we need because we 633 00:36:15,850 --> 00:36:17,800 wanted to once we see it like these 634 00:36:17,800 --> 00:36:20,200 transformations working out right. What we have, 635 00:36:20,380 --> 00:36:23,470 we have the transformation, we have the set of 636 00:36:23,650 --> 00:36:26,890 data or the I mean in signals or the data doesn't 637 00:36:26,890 --> 00:36:29,050 matter, can be huge and can be anything. I don't 638 00:36:29,050 --> 00:36:33,820 care. So once you get that right, so you pass it 639 00:36:33,820 --> 00:36:36,370 through the transformation. These input data is 640 00:36:36,370 --> 00:36:40,060 transformed into the democratized version of the I 641 00:36:40,060 --> 00:36:42,850 mean, in this case, we only have real components. 642 00:36:42,850 --> 00:36:45,370 We don't even have a complex component that will 643 00:36:45,370 --> 00:36:48,330 say, look, that will say the complexity as well. 644 00:36:48,640 --> 00:36:52,720 Right. So these are some of the graphs based on 645 00:36:52,720 --> 00:36:57,880 the on the existing phragmites algorithm. This one 646 00:36:57,880 --> 00:37:02,090 is Ch'ing that's famous from Kyon, Taisha and then 647 00:37:02,090 --> 00:37:06,130 the DCD. This is a proposed one. This is Arang 648 00:37:06,220 --> 00:37:09,910 paper, and this one is another one that we have 649 00:37:09,910 --> 00:37:13,630 done with my advisor anyway. So if you look at it, 650 00:37:13,840 --> 00:37:16,030 look at this one cluster of additions is not that 651 00:37:16,030 --> 00:37:18,580 good, to be honest. I mean, there are better ones, 652 00:37:18,580 --> 00:37:22,860 right? In this was Blomkamp one is better, but I 653 00:37:22,860 --> 00:37:25,900 worry about the cost of rendition. No, I don't 654 00:37:25,930 --> 00:37:29,330 like the additions corresponding to the Adesina in 655 00:37:29,350 --> 00:37:32,800 a circuit design point of view or in like how we 656 00:37:32,890 --> 00:37:36,910 design this integrated. It's all a very large VLSI, 657 00:37:36,920 --> 00:37:41,180 very large integrated circuit implementation, so 658 00:37:41,180 --> 00:37:44,320 indeed I'm not worried because it's cheap anyway. 659 00:37:44,510 --> 00:37:47,370 So do I worry about the multiplication? Yes, I do. 660 00:37:47,670 --> 00:37:51,650 So the thing is, again, the I mean, the cost 661 00:37:51,650 --> 00:37:54,260 associated with the Multiplex's, like I said, ten 662 00:37:54,260 --> 00:37:58,580 thousand dollars. Say one. So you say more, right? 663 00:37:58,820 --> 00:38:00,910 I mean, not we don't want to say one anyway. 664 00:38:00,920 --> 00:38:04,070 Nobody's going to I mean give you I mean nobody 665 00:38:04,070 --> 00:38:07,700 wins except except if you say one anyway. So what 666 00:38:07,700 --> 00:38:11,090 I'm telling you is try to say as much as the 667 00:38:11,270 --> 00:38:14,900 multiplication complexity if you actually want to 668 00:38:15,440 --> 00:38:18,690 create a chip out of that, if you actually want to 669 00:38:18,710 --> 00:38:22,730 sell something. Right. So then this one is the 670 00:38:23,060 --> 00:38:25,400 drastic cut down and that's the lowest 671 00:38:25,580 --> 00:38:29,900 multiplicative complexity of the discrete, cosine 672 00:38:29,900 --> 00:38:33,540 principle technique in the literature. And see, 673 00:38:33,560 --> 00:38:36,020 that's what I said. So it goes like you have a 674 00:38:36,020 --> 00:38:38,010 signal coming from one direction, signal coming 675 00:38:38,080 --> 00:38:41,030 the other direction, you put it in there. And if 676 00:38:41,030 --> 00:38:44,210 those signals combine in pass at such debugging, 677 00:38:44,510 --> 00:38:47,900 the games get into the one those other Multiplex's 678 00:38:48,020 --> 00:38:51,440 again, you you pick the frequency. So you have the 679 00:38:51,440 --> 00:38:54,560 signal coming up. You put a multiplexed you pick 680 00:38:54,560 --> 00:38:57,440 up. Right. Or the split as you have a signal. 681 00:38:57,440 --> 00:38:59,960 Signal I mean signal coming through one direction. 682 00:38:59,960 --> 00:39:03,020 And then you split it and it goes like that. And 683 00:39:03,020 --> 00:39:06,960 then in a few times I know you have two main types. 684 00:39:07,020 --> 00:39:08,990 One is that information in time that you mentioned 685 00:39:08,990 --> 00:39:11,510 in frequency because you are playing from time 686 00:39:11,510 --> 00:39:13,490 domain to the frequency domain and frequency 687 00:39:13,490 --> 00:39:17,000 domain to the time doing. Once you have that, if 688 00:39:17,000 --> 00:39:19,760 you have one, so you assume you have a time domain 689 00:39:19,970 --> 00:39:22,040 data, you can get the frequency domain data 690 00:39:22,040 --> 00:39:24,560 because you just use that it was operations that 691 00:39:24,570 --> 00:39:27,980 simply. That's simple that much. OK, look at the 692 00:39:27,980 --> 00:39:31,160 signal graph. It's not complicated. It's I mean, 693 00:39:32,420 --> 00:39:34,820 if I mentioned the complicated version, if you 694 00:39:34,820 --> 00:39:37,700 remember the deep neural network, if you will 695 00:39:37,700 --> 00:39:40,790 think about that, when you have a fully connected, 696 00:39:40,790 --> 00:39:44,150 deep neural network, each and every signalling 697 00:39:44,150 --> 00:39:49,280 here has to be connect with each and every thing. 698 00:39:49,760 --> 00:39:52,790 That's what we mean. The brute force calculation. 699 00:39:53,000 --> 00:39:55,550 If I use a brute force calculation, if I didn't 700 00:39:55,550 --> 00:39:58,370 propose a sports factorization, if I didn't reduce 701 00:39:58,370 --> 00:40:01,340 the complexity, that's what I have is a fully 702 00:40:01,340 --> 00:40:05,390 connected neural network. So I don't need that. If 703 00:40:05,390 --> 00:40:07,520 it is fully connected, we're going to we're going 704 00:40:07,520 --> 00:40:10,220 to do that. I mean, who want to buy it, right? 705 00:40:10,220 --> 00:40:12,170 Nobody going to buy it. And we don't want it to 706 00:40:12,170 --> 00:40:14,810 produce like a hundred thousand. I don't know, a 707 00:40:14,990 --> 00:40:18,200 single chip is like that. So over the phone, like 708 00:40:18,200 --> 00:40:20,210 we cannot even buy a phone for a thousand dollars. 709 00:40:20,210 --> 00:40:21,710 We would buy a phone for a hundred thousand 710 00:40:21,710 --> 00:40:24,110 dollars, which we don't need it. So nobody going 711 00:40:24,110 --> 00:40:26,150 to do that. I mean, nobody is willing to buy 712 00:40:26,150 --> 00:40:29,350 something like that. So OK, anyway, so if you use 713 00:40:29,360 --> 00:40:31,490 a brute force calculation or if you have a fully 714 00:40:31,490 --> 00:40:34,790 connected neural network in that, I mean, in a 715 00:40:34,790 --> 00:40:37,760 sense of neural network point of view. So what you 716 00:40:37,760 --> 00:40:41,930 have said you will have if it is eight signals, 717 00:40:41,930 --> 00:40:44,510 right. If there are eight signals coming, but he 718 00:40:44,570 --> 00:40:46,820 only eight signals, but it can be anything. Keep 719 00:40:46,820 --> 00:40:49,400 that in your mind. Right. Since it is a 50 type 720 00:40:49,400 --> 00:40:52,400 algorithm, these signals has to be the power of 721 00:40:52,400 --> 00:40:55,610 two. Right. Otherwise it won't run through the 722 00:40:55,610 --> 00:40:57,950 radix to algorithm. By the way, it seems we have 723 00:40:57,950 --> 00:41:01,190 the right to algorithmic around three of or the 724 00:41:01,190 --> 00:41:04,670 ratings for algorithm or the split radix. What are 725 00:41:04,670 --> 00:41:07,370 we looking you can develop from this algorithm 726 00:41:07,520 --> 00:41:10,890 anyway. So if you have a fully connected signal 727 00:41:10,890 --> 00:41:14,690 for graph in there, we need if we are if there are 728 00:41:14,690 --> 00:41:17,510 eight signals coming in and then eight signals 729 00:41:17,510 --> 00:41:20,930 coming out, they are we need eight times eighty, 730 00:41:20,940 --> 00:41:24,650 sixty four Multiplex's. See how many Multiplex's I 731 00:41:24,650 --> 00:41:28,010 use. One, two, three, four, five, six, seven, 732 00:41:28,010 --> 00:41:33,260 eight, nine, 10, 11. So 11 multiplexed as opposed 733 00:41:33,260 --> 00:41:35,660 to sixty four Multiplex's. This is only four eight 734 00:41:35,660 --> 00:41:39,260 by eight. Guess how much drastic cut down in that 735 00:41:39,500 --> 00:41:42,830 complexity or the multiplier accumulation you need. 736 00:41:42,830 --> 00:41:45,680 So you have all of these units. I cumulated with 737 00:41:45,680 --> 00:41:48,230 each other this negative one. These are like a 738 00:41:48,650 --> 00:41:51,440 like a timestamp. So what do you do in electrical 739 00:41:51,440 --> 00:41:53,720 engineering point of view? You take the wire and 740 00:41:53,720 --> 00:41:57,470 then you like like a C once the signal goes to 741 00:41:57,470 --> 00:41:59,780 your take away and you connect it to some some 742 00:41:59,780 --> 00:42:02,570 signal coming before that. That's what that's what 743 00:42:02,570 --> 00:42:05,480 they do in an engineering point of view. Anyway, 744 00:42:05,630 --> 00:42:08,750 that's negative one percent. Right. So these are I 745 00:42:08,750 --> 00:42:11,880 mean, you take a bullet and then you take a bypass 746 00:42:11,900 --> 00:42:14,030 and you've been a good. Yeah, that's what you do. 747 00:42:14,600 --> 00:42:18,080 It's not expensive. It's just the way anyway. So 748 00:42:18,080 --> 00:42:19,640 it's a you don't need a management excess. That's 749 00:42:19,640 --> 00:42:23,120 a good thing. So so it's a nice and beautiful. So 750 00:42:23,120 --> 00:42:25,790 you have butterfly structure. I mean, I mean not 751 00:42:25,790 --> 00:42:28,910 exactly butterfly structure of the DFT, but you 752 00:42:28,910 --> 00:42:31,580 see you have a butterfly in here. Butterflies, the 753 00:42:31,580 --> 00:42:34,660 butterfly s.a. And these are butterflies. Extra 754 00:42:34,660 --> 00:42:38,310 steps. But I mean, it's not that bad. I mean, it's 755 00:42:38,330 --> 00:42:41,170 really good in complex the point of view, because, 756 00:42:41,170 --> 00:42:43,570 I mean, there were no such multiplicative 757 00:42:43,570 --> 00:42:47,670 complexity, be this them and then this is 14 less, 758 00:42:47,680 --> 00:42:50,800 because once once you have signals, right, once 759 00:42:50,800 --> 00:42:53,770 you transform signal into the certain like a 760 00:42:53,770 --> 00:42:57,070 transform, better assume in some case you want to 761 00:42:57,070 --> 00:42:59,200 recover the original signal. OK, how can you 762 00:42:59,200 --> 00:43:02,050 recover that? So you have the process truly must 763 00:43:02,050 --> 00:43:05,260 transform or you have to design a circuit so that 764 00:43:05,260 --> 00:43:09,880 you could this this signal or the integrated 765 00:43:09,880 --> 00:43:12,850 circuit design and then so that you can recover 766 00:43:12,850 --> 00:43:15,640 the original signal. The original signal is not 767 00:43:15,640 --> 00:43:18,880 easy. Go right anyway. So that kind of also can be 768 00:43:18,880 --> 00:43:21,910 done very efficiently. Like a to again sixty four. 769 00:43:21,910 --> 00:43:24,790 I have one, two, three, four, five, six, seven, 770 00:43:24,790 --> 00:43:30,880 eight, nine, ten, eleven. Which is quite good. OK, 771 00:43:30,910 --> 00:43:34,630 so then OK, for the commercialization, OK, we have 772 00:43:34,630 --> 00:43:37,810 the circuit, that's a main part of it. And then 773 00:43:37,970 --> 00:43:41,570 for again, for the jetpack and IMPAC people, OK, 774 00:43:41,590 --> 00:43:44,140 they are interested about image compression or the 775 00:43:44,140 --> 00:43:47,290 restoration or the reconstruction thereof. 776 00:43:47,290 --> 00:43:49,810 Conversation techniques. You can have a frequency 777 00:43:49,810 --> 00:43:53,170 conversation or the conversation or the 778 00:43:53,170 --> 00:43:56,740 conversation metrics. What we did here was the 779 00:43:56,740 --> 00:44:00,820 color composition and a quantization matrix. Those 780 00:44:00,820 --> 00:44:04,240 are the two things that I use in here. So if you 781 00:44:04,510 --> 00:44:06,640 forget about anything, right, if you take Matlab 782 00:44:06,640 --> 00:44:09,880 so they have the image of compression results, if 783 00:44:09,880 --> 00:44:13,270 you do it, you can use the DVD for that one. You 784 00:44:13,270 --> 00:44:16,330 know that that one used the full matrix, which is 785 00:44:16,330 --> 00:44:20,200 computationally I mean, huge burden. And even if 786 00:44:20,200 --> 00:44:24,040 you like the coding python or see if you use the 787 00:44:24,040 --> 00:44:27,370 brute force matrix, it's again the complexities 788 00:44:27,370 --> 00:44:31,000 drastically growth, I mean increase. So we don't 789 00:44:31,000 --> 00:44:34,270 need that. So what we do is we have this little 790 00:44:34,270 --> 00:44:37,240 complexity algorithm, so we let's use that one. 791 00:44:37,240 --> 00:44:41,410 Why not? And so if the match if you can see the 792 00:44:41,410 --> 00:44:43,510 image, we can look at the quality of the image. 793 00:44:43,510 --> 00:44:46,390 Right. So image quality is not defined. How you 794 00:44:46,390 --> 00:44:49,080 see that object mentioned like a detailed 795 00:44:49,110 --> 00:44:52,210 measurements. Those determinations depend on the 796 00:44:52,840 --> 00:44:55,930 Senate, which is a big signal to noise ratio or 797 00:44:56,090 --> 00:44:59,130 same structure, similar to being the measurement. 798 00:44:59,410 --> 00:45:02,540 If you can get one or you're not losing any of the 799 00:45:02,590 --> 00:45:05,170 grade, you recover all of the information that you 800 00:45:05,170 --> 00:45:07,930 had. That's nice. And B, isn't that A high the 801 00:45:07,930 --> 00:45:10,360 percent not a better the quality that you can 802 00:45:10,360 --> 00:45:12,700 recognize. That's how it test. But you don't want 803 00:45:12,700 --> 00:45:15,850 it to go like beyond beyond this. OK, if you can 804 00:45:16,090 --> 00:45:19,390 that go that mean scratchiness and misses that. 805 00:45:19,390 --> 00:45:23,410 And then the same people believe that you cannot 806 00:45:23,410 --> 00:45:27,370 judge, you cannot check the quality of the image 807 00:45:27,370 --> 00:45:30,700 only by using visual comparison. You have to have 808 00:45:30,700 --> 00:45:33,910 an object comparison aspect that was shown by 809 00:45:34,570 --> 00:45:40,040 James Nogi. I mean, he was the more he was the. He 810 00:45:40,040 --> 00:45:42,320 was the head of the department anymore anyway, so 811 00:45:42,320 --> 00:45:44,270 he's the one who mentioned that, OK, you cannot 812 00:45:44,270 --> 00:45:47,540 have the visual comparison to analyze the quality. 813 00:45:47,570 --> 00:45:50,270 We have to consider the object measurements and 814 00:45:50,270 --> 00:45:52,370 then we have to introduce some noise in there. 815 00:45:52,400 --> 00:45:57,500 They wrote a really nice image. It's very nice be. 816 00:45:58,040 --> 00:46:01,340 And like how they introduce all the noises and all 817 00:46:01,340 --> 00:46:04,310 these very nice, beautiful book. Anything that was 818 00:46:04,310 --> 00:46:08,000 somewhere in two thousand six or something, 2005 819 00:46:08,000 --> 00:46:11,740 or 2006, something like that. Anyway, so it's a 820 00:46:11,750 --> 00:46:14,030 structure Simonetta index measure, one that depend 821 00:46:14,030 --> 00:46:16,910 on the illuminated contrast and a structure to. 822 00:46:17,090 --> 00:46:18,980 Yes, they are important. Right. If you want if you 823 00:46:18,980 --> 00:46:21,470 watch a TV, you will see that there are like all 824 00:46:21,470 --> 00:46:24,770 these terms that you can change the contrast and 825 00:46:24,770 --> 00:46:27,630 the luminous luminosity and all of these. Look at 826 00:46:27,630 --> 00:46:30,050 this hand, this image. This is not my image of 827 00:46:30,050 --> 00:46:32,240 this image I found online, which is five by two, 828 00:46:32,240 --> 00:46:36,290 up by five by 12 times three. OK, I like it 829 00:46:36,290 --> 00:46:38,900 because it has a brain and the people use food 830 00:46:38,900 --> 00:46:43,280 that people use this DVD in the image restoration 831 00:46:43,280 --> 00:46:46,640 in in those things. So I like that one. So that's 832 00:46:46,640 --> 00:46:49,220 why I use it. Right. This one. This one is using 833 00:46:49,220 --> 00:46:51,530 the encoding stage. Look at the image in the 834 00:46:51,530 --> 00:46:54,800 encoding stage, say look at this one. Like what I 835 00:46:54,800 --> 00:46:57,650 did was, OK, keep it in your mind. Any image, 836 00:46:57,650 --> 00:47:02,030 anything that you see in the TV. Indeed, if you 837 00:47:02,030 --> 00:47:06,260 disguise it, that's a matrix. Actually, any image 838 00:47:06,260 --> 00:47:08,750 is a matrix. It can be a square. It can be a 839 00:47:08,750 --> 00:47:12,800 rectangular, rectangular. Any discrete image is a 840 00:47:12,800 --> 00:47:15,920 matrix. It's there. So then what I did here, OK, I 841 00:47:15,920 --> 00:47:20,470 have the matrix associated with image I d critize 842 00:47:20,810 --> 00:47:23,480 say it's a five by 12 highlighted image by two and 843 00:47:23,480 --> 00:47:26,150 five times three, which is IGB component Deeney. 844 00:47:26,630 --> 00:47:29,810 So I this goes into the eight by eight blocks and 845 00:47:29,810 --> 00:47:32,890 then I how the my crosswell. I take the block 846 00:47:32,900 --> 00:47:35,930 product with the cross that I introduce. I mean 847 00:47:35,930 --> 00:47:39,050 it's not that easy but it's OK so I have to tell 848 00:47:39,060 --> 00:47:43,100 something to make everybody understand anyway. So 849 00:47:43,100 --> 00:47:45,680 then I take the block product in individual those 850 00:47:45,680 --> 00:47:49,340 blocks. Right. And I translate into the encoding 851 00:47:49,340 --> 00:47:52,640 station. This is the image in the encoding stage 852 00:47:52,940 --> 00:47:55,760 and then I use you remember I said that if I 853 00:47:55,760 --> 00:47:58,310 wanted to get the original guy that I need the 854 00:47:58,310 --> 00:48:02,510 inverse BCT, which is the three I hit with that 855 00:48:02,510 --> 00:48:06,620 one. And then I got this image back in the 856 00:48:06,620 --> 00:48:10,940 decoding state since I use the color, I mean, what 857 00:48:10,940 --> 00:48:15,530 is that? Quantization and also just quantization? 858 00:48:15,530 --> 00:48:18,410 I can I could not recover the color composition in 859 00:48:18,420 --> 00:48:21,440 hizzy. So this one is like that. This is this is 860 00:48:21,440 --> 00:48:24,380 not colored one. Right anymore because I already 861 00:48:24,380 --> 00:48:27,560 lost some information, but it's not that bad. The 862 00:48:27,560 --> 00:48:31,010 system is perfect when I look at it because I just 863 00:48:31,010 --> 00:48:33,980 kind of like this one into the grayscale image. So 864 00:48:33,980 --> 00:48:36,630 I come back. This is a I based on the grayscale 865 00:48:36,630 --> 00:48:38,900 and that's why I got this one. Otherwise I want 866 00:48:39,440 --> 00:48:43,070 right. And this one is my RGV. Look at the RGV. 867 00:48:43,220 --> 00:48:46,940 You don't see this one. See the AGB of this image. 868 00:48:47,420 --> 00:48:50,540 You don't see this one to your naked eye unless 869 00:48:50,540 --> 00:48:52,880 you run to a specific out there. And this is the 870 00:48:52,880 --> 00:48:55,850 spectrum frequency spectrum of this. And these are 871 00:48:56,030 --> 00:49:00,050 associated with my boy officiants. Those are not 872 00:49:00,050 --> 00:49:03,110 from the brute force, but through the proposed 873 00:49:03,240 --> 00:49:06,530 algorithm. See, these are nice, beautiful spread 874 00:49:06,530 --> 00:49:10,070 out. These are gibi. I mean, red, blue and green 875 00:49:10,550 --> 00:49:14,270 is nice and I love it. And this one is the photo 876 00:49:14,270 --> 00:49:16,820 that my husband took me. This is actually NIPA 877 00:49:16,820 --> 00:49:20,880 Spear, so I actually have that one as one in one 878 00:49:20,900 --> 00:49:24,980 of my pictures as well. So anyway, so he do this 879 00:49:25,310 --> 00:49:28,520 figure and I love that, so I could then I said I 880 00:49:28,520 --> 00:49:30,690 OK, I wanted to test that one for one of my other. 881 00:49:30,720 --> 00:49:33,290 Don't let me do that. So then in this case of the 882 00:49:33,320 --> 00:49:36,060 things I already have that in the previous image. 883 00:49:36,080 --> 00:49:38,000 Look at it. I didn't introduce any noise. This is 884 00:49:38,030 --> 00:49:40,940 existant. Imaginary. OK, this time what I do is 885 00:49:41,510 --> 00:49:43,420 I'm going to introduce some noise. Think that 886 00:49:43,550 --> 00:49:47,540 because any image has the noisy name, any like 887 00:49:47,540 --> 00:49:49,880 anything that you talk about has a noise we need. 888 00:49:50,240 --> 00:49:52,910 So we cannot we cannot fully recover. Noise 889 00:49:52,910 --> 00:49:55,550 component is always there to the nicely because I 890 00:49:55,630 --> 00:49:58,430 do white goes in noise so the noise will be like a 891 00:49:58,430 --> 00:50:01,100 nice, beautiful, normal distribution at the end. 892 00:50:01,430 --> 00:50:03,420 You didn't I mean you don't need to consider Bod 893 00:50:03,500 --> 00:50:06,950 like a Bjorn Tasikmalaya. I'm in school. Said they 894 00:50:06,970 --> 00:50:10,190 need me. Right. So then I added some noise and 895 00:50:10,340 --> 00:50:13,490 that's why this one we cannot even see it. This 896 00:50:13,490 --> 00:50:16,100 image in the encoding stage, it came from this one 897 00:50:16,390 --> 00:50:20,030 not because I added some noise. So how much I did 898 00:50:20,060 --> 00:50:22,990 I only transmit at this eighty seven point five. 899 00:50:23,180 --> 00:50:26,210 So I simply introduce noise for the remaining part, 900 00:50:26,210 --> 00:50:29,420 which is whatever that is. Right, whatever. One 901 00:50:29,420 --> 00:50:31,940 hundred minus this one, which is twelve point five 902 00:50:32,450 --> 00:50:36,440 anyway. So that one noise, this noise, this twelve 903 00:50:36,440 --> 00:50:38,630 point five noise was also introducing each and 904 00:50:38,630 --> 00:50:43,510 every block. Right, because I ran to the isolation 905 00:50:43,510 --> 00:50:46,540 of the eight by eight, I mean, why are you then 906 00:50:46,540 --> 00:50:48,430 you might be questioned why you will have to run 907 00:50:48,520 --> 00:50:51,520 for a bread. You can run it for discrediting 16 by 908 00:50:51,520 --> 00:50:57,790 16 or 32 by 32 or whatever that is. Right. And 909 00:50:57,790 --> 00:50:58,240 then. 910 00:51:04,360 --> 00:51:09,870 And then what we do is in here. So then I 911 00:51:09,870 --> 00:51:11,670 introduced that one, OK, then look at it, I 912 00:51:11,670 --> 00:51:15,240 reconstructed I mean, it's not I mean, it's not 913 00:51:15,300 --> 00:51:17,910 that bad, but it's not that good either because of 914 00:51:17,910 --> 00:51:20,010 the noise, because of the noise. It's like a 915 00:51:20,010 --> 00:51:22,920 blurred image. That's why my piece and not be a 916 00:51:22,950 --> 00:51:26,240 signal to noise ratio is a little low. You 917 00:51:26,280 --> 00:51:28,170 remember I mentioned that person. I'd hire the 918 00:51:28,170 --> 00:51:31,110 person not with other qualities. When they say 919 00:51:31,120 --> 00:51:33,840 Siamese one, it's really good. If it is not, it's 920 00:51:33,840 --> 00:51:38,130 not good. So that tells us how we see through the 921 00:51:38,130 --> 00:51:41,190 naked eye with the object measurement because of 922 00:51:41,190 --> 00:51:46,020 the noise in the image. OK, so what do we do? How 923 00:51:46,020 --> 00:51:46,790 do we commercial. 924 00:51:49,790 --> 00:51:52,700 How do we commercialize this is one of the figures 925 00:51:52,700 --> 00:51:56,930 in the I mean, Payden anyway, so then this is how 926 00:51:56,970 --> 00:52:01,250 the DVD release circuitry in him, and then this 927 00:52:01,250 --> 00:52:07,150 one is the CBO. And then this one is the what is 928 00:52:07,170 --> 00:52:11,430 that one? Let me look at that one is a memory and 929 00:52:11,430 --> 00:52:15,270 this is the digital signal processing. OK, so we 930 00:52:15,270 --> 00:52:19,610 can we can put this reduce multiplication to DC 931 00:52:19,620 --> 00:52:25,800 three as a module, either in C.P.U or I think 932 00:52:25,800 --> 00:52:28,410 digital signal processing unit. And then what do 933 00:52:28,410 --> 00:52:31,410 we have here? This is a drone, right? So once we 934 00:52:31,410 --> 00:52:35,120 have this one, we decide you design the chip. 935 00:52:35,130 --> 00:52:38,330 Right. So you design the chip or you decided to 936 00:52:38,340 --> 00:52:42,330 give a circuit or whatever it is. And you include 937 00:52:42,330 --> 00:52:45,000 that in a drone who can include that in a drone or 938 00:52:45,030 --> 00:52:48,000 this is not growing into a scalar. Right. So you 939 00:52:48,000 --> 00:52:50,820 include that running the drone or you include that 940 00:52:50,820 --> 00:52:54,210 one in your phone or the tablet or whatever it is. 941 00:52:54,210 --> 00:52:57,120 You included that. Right. And then what these 942 00:52:57,120 --> 00:52:59,880 drones do, they capture the signals. Right. And 943 00:52:59,880 --> 00:53:03,390 this is the station, which is a radio frequency 944 00:53:03,390 --> 00:53:06,330 transmitting station. They capture the signal 945 00:53:06,540 --> 00:53:09,420 right through the sensors. Right. And then once 946 00:53:09,420 --> 00:53:13,650 they captured it, OK, we process this DCT through. 947 00:53:13,650 --> 00:53:15,510 Either you can process it. I think that you can 948 00:53:15,510 --> 00:53:17,790 process it to the area or you can process it. The 949 00:53:17,990 --> 00:53:21,000 battle would be beautiful if you could do that. So 950 00:53:21,000 --> 00:53:24,150 you process it by using the reduction of 951 00:53:24,150 --> 00:53:29,070 multiplexing. You watch that accumulation unit and 952 00:53:29,070 --> 00:53:32,670 then say these are the frequency descriptions. You 953 00:53:32,670 --> 00:53:34,920 remember I said that we need to use these 954 00:53:34,920 --> 00:53:37,050 transform. You can go for the frequency domain and 955 00:53:37,050 --> 00:53:39,090 time domain. So this is a time domain. The 956 00:53:39,090 --> 00:53:42,840 snapshot goes into the frequency domain, frequency 957 00:53:42,840 --> 00:53:45,240 domain distribution. And then this is the 958 00:53:45,390 --> 00:53:48,940 compressed image based on what you get. I mean, 959 00:53:48,990 --> 00:53:51,210 detailed information on here, what I mentioned, 960 00:53:51,210 --> 00:53:53,520 how how to compress it. That's what I mentioned in 961 00:53:53,520 --> 00:53:56,610 a couple of previous one. And then to design this 962 00:53:56,610 --> 00:53:59,730 chip, that's how I lay out how the signals need to 963 00:53:59,730 --> 00:54:01,920 go through through the signal. This is true. The 964 00:54:01,920 --> 00:54:06,510 signal program and this is the image, image, image 965 00:54:06,510 --> 00:54:10,020 compression, image recognition one. So you have 966 00:54:10,020 --> 00:54:12,960 the data, you have a set of input data and you 967 00:54:12,960 --> 00:54:16,200 have the multiplicative accumulator you need. But 968 00:54:16,200 --> 00:54:18,540 you reduction with the reduction of complexity. 969 00:54:18,810 --> 00:54:22,560 You're only serial or the parallel to your chip or 970 00:54:22,560 --> 00:54:27,210 domain as a module in the in the C.P.U or in the 971 00:54:27,570 --> 00:54:31,650 in the DSP digital signal processing unit. So then 972 00:54:31,650 --> 00:54:36,450 you have the companies emerging there. And then 973 00:54:36,450 --> 00:54:39,060 what we have proposed, we have proposed orthogonal 974 00:54:39,060 --> 00:54:41,820 transform phones for the community, high 975 00:54:41,820 --> 00:54:46,190 efficiency, geocoding, and they use DCG to NBC 976 00:54:46,380 --> 00:54:49,440 three as a optima transform. And that's why it's 977 00:54:49,440 --> 00:54:51,480 important for the Hibat community and of course 978 00:54:51,480 --> 00:54:54,300 for the vision impaired community as well. And 979 00:54:54,300 --> 00:54:57,090 then these are the lowest multiple video 980 00:54:57,720 --> 00:55:00,360 accumulation units in a digital signal processing. 981 00:55:00,360 --> 00:55:03,600 And then we have designed the customized 982 00:55:03,600 --> 00:55:08,610 integrated circuits for the commercial device. And 983 00:55:08,790 --> 00:55:12,610 these are a couple couple of papers that relate to 984 00:55:12,960 --> 00:55:18,330 this work. And then let me quickly show the Payden. 985 00:55:22,050 --> 00:55:25,300 And this is the actual patented with. 986 00:55:38,000 --> 00:55:42,890 Now, that's a burden, so. So so it was intended a 987 00:55:42,890 --> 00:55:47,390 process by by this one, and I actually submit this 988 00:55:47,390 --> 00:55:50,930 one the day before I went to the hospital, I mean 989 00:55:50,930 --> 00:55:54,470 to that I mean, so my university submitted on 990 00:55:54,470 --> 00:55:57,590 November 30th, 2007, just the day after Dohan was 991 00:55:57,590 --> 00:56:03,340 born. So any took like. Three more than three 992 00:56:03,340 --> 00:56:06,850 years. To process that because they have to go 993 00:56:06,850 --> 00:56:09,070 through the whole process and this is like a. 994 00:56:11,540 --> 00:56:16,190 And then explanation of the. And that's it, and 995 00:56:16,190 --> 00:56:18,590 thank you so much for your attention, I appreciate 996 00:56:18,590 --> 00:56:21,080 it and thank you, Stephanie. And thank you, Laura, 997 00:56:21,560 --> 00:56:23,870 for organizing and I appreciate it. And thank you 998 00:56:23,870 --> 00:56:27,170 for all the support given by my department and and 999 00:56:27,170 --> 00:56:30,830 everybody who hired me to come this far. And I 1000 00:56:30,830 --> 00:56:34,010 truly appreciate everything you all have done for 1001 00:56:34,010 --> 00:56:38,870 me to come this far. Thank you, Richard. Thank you 1002 00:56:38,870 --> 00:56:41,210 very much for the very interesting talk. I will 1003 00:56:41,210 --> 00:56:43,940 ask the audience if they have questions and then 1004 00:56:43,940 --> 00:56:46,580 at the end, I will ask you a few questions. But 1005 00:56:46,580 --> 00:56:50,210 first, I want our guests to ask questions. 1006 00:56:55,290 --> 00:56:57,720 So let's let me take you what you learned about 1007 00:56:57,720 --> 00:57:03,080 this, OK? OK. The guests, not your. 1008 00:57:05,900 --> 00:57:07,040 So what questions do you have? 1009 00:57:10,250 --> 00:57:16,070 One classroom, OK, one oh, yeah, so am I, my 1010 00:57:16,130 --> 00:57:20,030 experience in our signal processing. So I don't 1011 00:57:20,030 --> 00:57:25,200 know why to makes sense or not. So mine is the 1012 00:57:25,220 --> 00:57:28,640 information processing is like two-stage the into 1013 00:57:28,640 --> 00:57:32,900 the signal encoded on to some form of behavior and 1014 00:57:32,900 --> 00:57:37,970 then decoding output signal. And I'm trying to 1015 00:57:37,970 --> 00:57:42,320 understand all the other all the results is is 1016 00:57:42,320 --> 00:57:47,260 applied to which state or both I want. OK, OK. In 1017 00:57:47,270 --> 00:57:50,000 the encoding. So you remember, you remember. I 1018 00:57:50,000 --> 00:57:52,820 mentioned about that. It's like the encoding and 1019 00:57:52,820 --> 00:57:56,540 then there are two versions. One, this one is for 1020 00:57:56,540 --> 00:58:01,010 the DC to do HSF, the other one is a DC three. 1021 00:58:01,250 --> 00:58:04,190 These three decided to use the forward process for 1022 00:58:04,190 --> 00:58:07,610 the encoding. So DC three is the one that we use 1023 00:58:07,610 --> 00:58:10,160 in the recording process because you remember, we 1024 00:58:10,160 --> 00:58:13,970 have to recover all the restore order. I mean, 1025 00:58:13,970 --> 00:58:17,870 reconstruct the image. So you have to use both in 1026 00:58:18,330 --> 00:58:24,050 the one, you use one. OK, I think I have just one 1027 00:58:24,050 --> 00:58:27,080 more question, which might be very general. And 1028 00:58:27,530 --> 00:58:31,580 the the so what kind of representation can be 1029 00:58:31,580 --> 00:58:33,240 considered as a good one? 1030 00:58:35,420 --> 00:58:39,950 So the representation that is hoping, like the 1031 00:58:39,950 --> 00:58:43,750 middle layer, the more the more displacement 1032 00:58:43,790 --> 00:58:46,850 mattresses that you could do, the better, the 1033 00:58:46,970 --> 00:58:49,810 better the quality, because if you use a full 1034 00:58:49,820 --> 00:58:51,980 matrix, because the noise coming through, because 1035 00:58:52,310 --> 00:58:55,660 if the matrix is dense or the feel good about it, 1036 00:58:55,670 --> 00:58:57,410 right. You have the noise associated with 1037 00:58:57,410 --> 00:58:59,810 everything and you will do like a more more 1038 00:58:59,810 --> 00:59:02,420 computational, more computation. I mean, like I 1039 00:59:02,420 --> 00:59:04,520 said. Right. So, you know, you always need to 1040 00:59:04,520 --> 00:59:07,370 think about the computational point of view and 1041 00:59:07,370 --> 00:59:09,840 then the signal processing point of view. Right. 1042 00:59:09,890 --> 00:59:13,820 So more you use the computational or more you use 1043 00:59:13,820 --> 00:59:17,330 of brute force or the full matrix is worst, you're 1044 00:59:17,330 --> 00:59:20,480 going to do it. So that's what I said in Matlab, 1045 00:59:20,480 --> 00:59:23,890 the median function, if you use just the DCD, the 1046 00:59:24,140 --> 00:59:26,210 building function in Matlab, they use the full 1047 00:59:26,210 --> 00:59:29,180 matrix. I mean, if you code by using by then we'll 1048 00:59:29,180 --> 00:59:32,660 see if you use a brute force for Matrix, it's it's 1049 00:59:32,660 --> 00:59:35,030 not going to give you a nice, impressive results. 1050 00:59:35,030 --> 00:59:37,480 It won't be clear once you reconstruct that mean 1051 00:59:37,490 --> 00:59:40,130 it won't be clean for the naked eye. And also if 1052 00:59:40,130 --> 00:59:42,320 you look at the object measurements like the 1053 00:59:42,330 --> 00:59:47,140 Senate or the exam, that one gives us impressive 1054 00:59:47,150 --> 00:59:50,540 results either. So if you could get rid of bias 1055 00:59:50,540 --> 00:59:53,990 and not hide the person and that is better. And 1056 00:59:53,990 --> 00:59:57,350 then if it's a siyam, if it is closer to one, it's 1057 00:59:57,350 --> 01:00:01,720 better. That's what it says. Because of my 1058 01:00:01,720 --> 01:00:08,670 question. OK, thank you. OK, thank you. To have 1059 01:00:08,760 --> 01:00:11,400 that comment, I don't know how to ask a question 1060 01:00:11,400 --> 01:00:16,220 like like I know so little in the detail, but not 1061 01:00:16,220 --> 01:00:20,190 to Reanna. You connect your algorithm in the 1062 01:00:20,190 --> 01:00:24,300 mathematics suicide, but to the heart, the were 1063 01:00:25,320 --> 01:00:29,340 construction crews that process. And that's a long 1064 01:00:29,340 --> 01:00:32,010 stretch. And you make this accessible. That's 1065 01:00:32,010 --> 01:00:35,280 amazing. Not in many of those research these days. 1066 01:00:35,640 --> 01:00:41,250 Connecticut today, but of course, the detail is 1067 01:00:41,340 --> 01:00:44,400 the table. I needed to know exactly this was going 1068 01:00:44,400 --> 01:00:47,670 to take another five years. But however, it's a 1069 01:00:47,670 --> 01:00:52,170 very interesting to you to start with. And we had 1070 01:00:52,230 --> 01:00:55,900 connected to what is the frontier interest in this 1071 01:00:55,900 --> 01:01:00,360 space with that natural gas computation and then 1072 01:01:00,360 --> 01:01:03,340 go to the hardware. That's the thing that make it 1073 01:01:03,340 --> 01:01:07,380 a different this the pattern that's very rare. 1074 01:01:07,680 --> 01:01:10,260 Good. The results I can you know, I hear for a 1075 01:01:10,260 --> 01:01:14,400 long time in that. Yeah. Thank you. Yeah. I don't 1076 01:01:14,400 --> 01:01:16,800 understand the detail, but however, I know the 1077 01:01:16,800 --> 01:01:18,750 significance because in the bigger Wikipedia 1078 01:01:19,020 --> 01:01:22,500 community, they keep talking and keep going to 1079 01:01:22,500 --> 01:01:28,640 have to talk a lot of ground to want to reduce 1080 01:01:28,770 --> 01:01:33,480 their sabbar computation computation. Because when 1081 01:01:33,480 --> 01:01:35,460 you do the natural language processing and the 1082 01:01:35,460 --> 01:01:39,150 image processing, a lot of natural gas and the 1083 01:01:39,150 --> 01:01:43,070 best of the cemetery and the 06. And how do you do 1084 01:01:43,070 --> 01:01:46,180 it by thousands and thousands? That's one of the 1085 01:01:46,260 --> 01:01:49,880 interesting yeah, that's true. They are like the 1086 01:01:49,880 --> 01:01:52,370 recent work going on. You know who I been, right? 1087 01:01:53,520 --> 01:01:56,400 You know, we've been right home hoping maybe, 1088 01:01:56,670 --> 01:02:01,770 maybe. No, no, you know him, you know you've got 1089 01:02:01,860 --> 01:02:06,430 Eubie. Oh, I have that in our department, in that 1090 01:02:06,440 --> 01:02:09,390 department. Yeah, yeah, yeah. Oh yeah, I hope so. 1091 01:02:09,600 --> 01:02:11,480 Yeah, yeah, yeah, yeah, 1092 01:02:14,930 --> 01:02:18,590 yeah. See, he say he in fact that they have a 1093 01:02:18,590 --> 01:02:23,570 problem, they have a problem in using a brute 1094 01:02:23,570 --> 01:02:26,510 force calculations or so they are interesting to 1095 01:02:26,510 --> 01:02:27,320 us, like you said, 1096 01:02:30,290 --> 01:02:33,200 to drive this fast factorization. Yeah. Yeah, yeah. 1097 01:02:33,230 --> 01:02:35,390 Because they are working on some problem that has 1098 01:02:35,390 --> 01:02:36,950 a brute force because this machine learning 1099 01:02:36,950 --> 01:02:39,950 process is expensive. Right. Because it's coming 1100 01:02:39,950 --> 01:02:42,320 through the training and then there are like a 1101 01:02:42,320 --> 01:02:45,740 transfer learning. Oh. Oh, that's a very expensive 1102 01:02:45,740 --> 01:02:48,560 process. So they are looking for this past 1103 01:02:48,590 --> 01:02:51,850 factorization so that they can reduce them. I mean, 1104 01:02:51,920 --> 01:02:54,740 complexity and machine learning process. So that 1105 01:02:54,740 --> 01:03:01,350 will speed up. Yeah, yeah, let's take another 1106 01:03:01,350 --> 01:03:04,850 question from Mitt Romney. Do you have a plan to 1107 01:03:05,640 --> 01:03:10,230 integrate those with them to make sure learning is 1108 01:03:11,190 --> 01:03:13,410 like a plan for the future? 1109 01:03:16,590 --> 01:03:21,810 Well, I certainly am asking all of this since I 1110 01:03:21,810 --> 01:03:25,980 know this. The procedure is kind of thing. I was 1111 01:03:25,980 --> 01:03:31,740 asking actually, if you have a plan to transfer 1112 01:03:31,740 --> 01:03:34,680 this, always an engineering thing, the framework 1113 01:03:34,720 --> 01:03:40,350 of learning later. Yeah, I know not to acid's I 1114 01:03:40,350 --> 01:03:44,610 have to do some some manipulations based on the 1115 01:03:44,610 --> 01:03:48,920 problem. So I mean, since it's already since he's 1116 01:03:48,930 --> 01:03:51,870 already published things, he's already been like, 1117 01:03:51,870 --> 01:03:54,600 say if you're going to write a proposal, they're 1118 01:03:54,600 --> 01:03:58,050 not going to fund for now one. So unless I do 1119 01:03:58,050 --> 01:04:02,220 something as or obtain some other factorization or 1120 01:04:02,220 --> 01:04:04,590 I proposed that one through the parallel process, 1121 01:04:04,800 --> 01:04:07,710 that will drastically cut down. Yes. In that sense, 1122 01:04:07,710 --> 01:04:12,190 yes. But not as it is, but in a different version. 1123 01:04:12,990 --> 01:04:16,800 It sounds very attractive. Thank you, Tim. 1124 01:04:19,400 --> 01:04:22,760 So we have a question from Horwitt. Yes, I think 1125 01:04:23,410 --> 01:04:27,530 it's in the text, in the chat. So it's about 12 of 1126 01:04:28,070 --> 01:04:31,280 factorization of the Matrix, if it's unique or not. 1127 01:04:31,390 --> 01:04:35,630 The four questions from yes, it is unique. And I'm 1128 01:04:35,630 --> 01:04:37,910 the one who developed one and only factorization. 1129 01:04:37,910 --> 01:04:42,320 It's unique. And then from the point of what I 1130 01:04:42,320 --> 01:04:44,790 don't understand. His second question then is the 1131 01:04:44,830 --> 01:04:48,120 second question. I think if it was not unique, if 1132 01:04:48,120 --> 01:04:51,140 he can be produced more by a factor of two or more, 1133 01:04:51,290 --> 01:04:56,000 if it is unique, it is unique. It's the one and 1134 01:04:56,000 --> 01:05:00,380 only and then the I don't know whether it has a 1135 01:05:00,380 --> 01:05:03,140 question similar to this, but if you need like say, 1136 01:05:03,140 --> 01:05:06,250 for example, we don't want to it to all the time. 1137 01:05:06,260 --> 01:05:10,610 Sometimes we need the split like a one goes to one 1138 01:05:10,610 --> 01:05:13,550 divide, like one said, one more sample in sample 1139 01:05:13,550 --> 01:05:16,610 divided into two, the other half divided into the 1140 01:05:16,610 --> 01:05:20,210 four and a four or the whole set divided by three 1141 01:05:20,210 --> 01:05:23,330 and a three and a three. So in that Russians can 1142 01:05:23,330 --> 01:05:25,340 be divided as the consequences of this 1143 01:05:25,340 --> 01:05:30,920 factorization. OK. The last one, which is more 1144 01:05:30,920 --> 01:05:33,410 expensive, additional multiplication, 1145 01:05:33,800 --> 01:05:37,820 multiplication, multiplication, is it really 1146 01:05:37,820 --> 01:05:43,010 expensive? It is not that expensive. I mean, like 1147 01:05:43,130 --> 01:05:46,400 because I like I said it, it's like a like a five 1148 01:05:46,400 --> 01:05:51,610 dollars maximum. Well, why not, it is the one on 1149 01:05:51,610 --> 01:05:54,460 my keys, in addition, I don't know why I took them 1150 01:05:54,460 --> 01:05:56,770 five dollars, but if they don't know 1151 01:05:56,770 --> 01:05:58,780 multiplication, I charge them fifty dollars. 1152 01:05:59,800 --> 01:06:00,850 That's a good point. 1153 01:06:04,660 --> 01:06:08,920 I have two questions. So first question, is the 1154 01:06:09,010 --> 01:06:12,820 cause of this compression property of this city 1155 01:06:12,820 --> 01:06:16,070 over DFT? Have you looked at this first method, 1156 01:06:16,070 --> 01:06:20,410 the order of magnetic resonance imaging MRI based 1157 01:06:20,410 --> 01:06:24,670 on the cosine transform? Know, because a lot of 1158 01:06:24,670 --> 01:06:30,430 applications in bayoumy redskins' required MRI? 1159 01:06:30,880 --> 01:06:35,260 Yes. And that's why I took that existing image. 1160 01:06:35,260 --> 01:06:39,070 And I, I, I applied my algorithm based on that 1161 01:06:39,070 --> 01:06:43,480 image and see. But I don't have a data other than 1162 01:06:43,480 --> 01:06:45,730 that. I have to work with the data associated with 1163 01:06:45,730 --> 01:06:51,550 that statement. So there is a group of problem and 1164 01:06:51,560 --> 01:06:56,450 I think also work with the data and then might be 1165 01:06:57,010 --> 01:07:00,120 can because you are telling them what I saw. It's 1166 01:07:04,180 --> 01:07:08,200 impossible. Yeah. And the second question that any 1167 01:07:08,200 --> 01:07:10,750 current devices which include this digital signal 1168 01:07:12,070 --> 01:07:14,410 that can facilitate efficient processing 1169 01:07:15,700 --> 01:07:18,640 techniques and this just appeared in January, we 1170 01:07:18,640 --> 01:07:24,580 are going to I have some I have I say 90. I cannot 1171 01:07:24,580 --> 01:07:29,280 talk about it. OK, well, I see. OK, interesting, 1172 01:07:29,290 --> 01:07:31,270 so you already got 1173 01:07:37,410 --> 01:07:39,940 me on the air and then you won't be here anymore, 1174 01:07:39,950 --> 01:07:40,240 right? 1175 01:07:43,390 --> 01:07:46,870 You guys have been talking a couple of minutes, 1176 01:07:46,870 --> 01:07:50,310 five minutes. So we have to stop right now and 1177 01:07:51,820 --> 01:07:56,080 you'll be there. OK, thank you. Thank you for any 1178 01:07:56,110 --> 01:07:58,570 good time. Thank you. Thank everybody for 1179 01:07:58,570 --> 01:08:02,170 attending and basically look for my e-mail for the 1180 01:08:02,170 --> 01:08:05,740 next week. OK, so every Thursday, 12 thirty is 1181 01:08:05,740 --> 01:08:09,430 like a new episode for the organizer and the 1182 01:08:09,710 --> 01:08:12,970 organizers, the guests and everybody else and the 1183 01:08:12,970 --> 01:08:17,560 speaker, of course. Thank you. Bye. Thank you so 1184 01:08:17,560 --> 01:08:20,650 much. Thank you. Thank you so much. Thank you, 1185 01:08:20,650 --> 01:08:24,610 everyone. I truly appreciate. My, my, my, my.