├── An Embedded Programmable Processor for Compressive.pdf ├── C++ ├── AMP.c ├── IHT.c ├── OMP.c ├── QR.c └── readme.md ├── LICENSE ├── MATLAB ├── AMP.m ├── IHT_Mine.m ├── OMP.m └── readme.md ├── README.md └── performance_comparison.png /An Embedded Programmable Processor for Compressive.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/NeuroFan/Compressive_Sensing_C_and_MATLAB/fc90eaaef090bc1a9cfa2698191c682425785998/An Embedded Programmable Processor for Compressive.pdf -------------------------------------------------------------------------------- /C++/AMP.c: -------------------------------------------------------------------------------- 1 | //Based on following MATLAB code 2 | /* 3 | Original Matlab Code 4 | r = y; 5 | s = zeros(n, 1); 6 | for iter = 1:iters 7 | pseudo_data = At*(r)+s; 8 | sigma_hat = sqrt(1 / m*sum(fabs(r). ^ 2)); 9 | s = (fabs(pseudo_data)> lambda*sigma_hat).*(fabs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 10 | r = y - A*(s)+1 / m.*r.*length(find(fabs(s)>0)); 11 | end 12 | x_hat = s; 13 | end*/ 14 | 15 | #include "math.h" 16 | #include 17 | #include 18 | 19 | #define M 64 // Number of measurement 20 | #define N 224 // Number of samples 21 | #define lambda 1.35 // lambda is determinded from exprimental data from RICE DSP github 22 | #define number_of_iterations 120 //self defined! 23 | 24 | int matMul(float *mat1, float *mat2, float *result, int m, int n, int q); 25 | int matMul_M(float *mat1, float *mat2, float *result, int m, int n, int q); //Matrix multipication with M being fixed (for loop unrolling) 26 | int matMul_N(float *mat1, float *mat2, float *result, int m, int n, int q); 27 | int transpose(float *mat1, float *mat2, int m, int n); 28 | int matSUB(float *mat1, float *mat2, float *result, int m, int n); //Matrix subtraction 29 | int matADD(float *mat1, float *mat2, float *result, int m, int n); //Matrix addition 30 | float norm2(float *vec); 31 | int print(float *mat, int m, int n); 32 | float sum_array(float *arr, int m); //Sum of elements of a vector 33 | float SNR(float *a, float *b, int Length); //Signal to Noise ratio 34 | float MSE(float *a, float *b, int Length); //Mean square error 35 | 36 | 37 | float sign(float input) 38 | { 39 | return (float)((0 < input) - (input < 0)); 40 | } 41 | 42 | int main() 43 | { 44 | 45 | //First we generate some test data for reconstruction part 46 | float A[M][N]; 47 | int i,j,k,K; 48 | int d; 49 | for (i = 0; i < M; i++) 50 | for (j = 0; j < N; j++){ 51 | int temp=0; 52 | //_TCE_RAND(1,temp); 53 | A[i][j] = (float)(rand()%3)-1; 54 | } 55 | 56 | float x[N], Y[M], At[N][M]; 57 | float middle_data[N], s[N], r[M], temp[M]; 58 | transpose((float *)A, (float *)At, M, N); 59 | float sigma; 60 | float Minve = 1 / (float)(M); 61 | float inv_sqrt_M = 1 / sqrtf(M); 62 | float inv_sqrt_N = 1 / sqrtf(N); 63 | float factor=lambda / sqrtf(M); 64 | 65 | //for (i = 1; i < M; i++) 66 | // for (j = 1; j < N; j++) 67 | // A[i][j] = (rand() % 2); // DO NOT USE THIS FUNCTION 68 | 69 | for (i = 0; i < M; i++) 70 | for (j = 0; j0) / m; 104 | for (i = 0; i < N; i+=8) 105 | { 106 | float mediatevalue1=fabs(s[i]) - astane; 107 | float mediatevalue2=fabs(s[i+1]) - astane; 108 | float mediatevalue3=fabs(s[i+2]) - astane; 109 | float mediatevalue4=fabs(s[i+3]) - astane; 110 | float mediatevalue5=fabs(s[i+4]) - astane; 111 | float mediatevalue6=fabs(s[i+5]) - astane; 112 | float mediatevalue7=fabs(s[i+6]) - astane; 113 | float mediatevalue8=fabs(s[i+7]) - astane; 114 | 115 | if (mediatevalue1>0) { s[i] = (mediatevalue1)*sign(s[i]);//s = (abs(pseudo_data)> lambda*sigma_hat).*(abs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 116 | b = b +1; }else s[i] = 0; 117 | 118 | if (mediatevalue2>0) { s[i+1] = (mediatevalue2)*sign(s[i+1]);//s = (abs(pseudo_data)> lambda*sigma_hat).*(abs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 119 | b = b +1;}else s[i+1] = 0; 120 | 121 | if (mediatevalue3>0){ s[i+2] = (mediatevalue3)*sign(s[i+2]);//s = (abs(pseudo_data)> lambda*sigma_hat).*(abs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 122 | b = b +1;}else s[i+2] = 0; 123 | 124 | if (mediatevalue4>0) { s[i+3] = (mediatevalue4)*sign(s[i+3]);//s = (abs(pseudo_data)> lambda*sigma_hat).*(abs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 125 | b = b +1;}else s[i+3] = 0; 126 | 127 | if (mediatevalue5>0) { s[i+4] = (fabs(s[i+4]) - astane)*sign(s[i+4]);//s = (abs(pseudo_data)> lambda*sigma_hat).*(abs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 128 | b = b +1;}else s[i+4] = 0; 129 | 130 | if (mediatevalue6>0) { s[i+5] = (fabs(s[i+5]) - astane)*sign(s[i+5]);//s = (abs(pseudo_data)> lambda*sigma_hat).*(abs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 131 | b = b +1;}else s[i+5] = 0; 132 | 133 | if (mediatevalue7>0) { s[i+6] = (fabs(s[i+6]) - astane)*sign(s[i+6]);//s = (abs(pseudo_data)> lambda*sigma_hat).*(abs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 134 | b = b +1;}else s[i+6] = 0; 135 | 136 | if (mediatevalue8>0) { s[i+7] = (fabs(s[i+7]) - astane)*sign(s[i+7]);//s = (abs(pseudo_data)> lambda*sigma_hat).*(abs(pseudo_data) - lambda*sigma_hat).*sign(pseudo_data); 137 | b = b +1;}else s[i+7] = 0; 138 | 139 | } 140 | // r = y - H*s + b.*r; 141 | b = b * Minve; ; 142 | matMul_N((float *)A, s, temp, M, N, 1); 143 | for (i = 0; i < M; i+=4){ 144 | r[i] = Y[i] - temp[i] + b*r[i]; 145 | r[i+1] = Y[i+1] - temp[i+1] + b*r[i+1]; 146 | r[i+2] = Y[i+2] - temp[i+2] + b*r[i+2]; 147 | r[i+3] = Y[i+3] - temp[i+3] + b*r[i+3]; 148 | } 149 | 150 | //if (MSE(s,x,N)<0.1) /////// BREAKING CONDITION 151 | // break; 152 | 153 | } 154 | } 155 | printf("Iteration Number: %d",ii); 156 | SNR(x,s,N); 157 | // print(s,1,N); 158 | // SNR(x,s,N); 159 | return(-1- 0); 160 | } 161 | 162 | 163 | 164 | 165 | 166 | int matSUB(float *mat1, float *mat2, float *result, int m, int n) { 167 | //Calculates mat1_m*n - mat2_m*n and reutrns the resultant matrix to result 168 | //Matrices should be the same size 169 | int i,j,k,K; 170 | for (i = 0; i < m; i++) { 171 | for (j = 0; j < n; j++) 172 | *(result + i*n + j) = *(mat1 + i*n + j) - *(mat2 + i*n + j); 173 | } 174 | return(0); 175 | } 176 | 177 | 178 | int matADD(float *mat1, float *mat2, float *result, int m, int n) { 179 | //Calculates mat1_m*n + mat2_m*n and reutrns the resultant matrix to result 180 | //Matrices should be the same size 181 | int i,j,k,K; 182 | for (i = 0; i < m; i++) { 183 | for (j = 0; j < n; j++) 184 | *(result + i*n + j) = *(mat1 + i*n + j) + *(mat2 + i*n + j); 185 | } 186 | return(0); 187 | } 188 | 189 | 190 | 191 | 192 | 193 | 194 | 195 | int matMul(float *mat1, float *mat2, float *result, int m, int n, int q) { 196 | //Multiplication for Mat1_(m*n) * Mat2_(n*k) 197 | // M,N and K are dimentions of matrices 198 | // Output is going to sit in the matrix that result represents here 199 | float sum; 200 | int i,j,k,K; 201 | for (i = 0; i < m; i++) { 202 | for (j = 0; j < q; j++) { 203 | sum = 0; 204 | for (k = 0; k < n; k++) { 205 | sum = sum + *(mat1 + i*n + k) * *(mat2 + k*q + j); 206 | } 207 | *(result + i*q + j) = sum; 208 | } 209 | } 210 | return(0); 211 | } 212 | 213 | int matMul_M( float *mat1, float *mat2, float *result, int m, int n, int q) { 214 | float sum1,sum2,sum3,sum4; 215 | int i,j,k,K; 216 | for (i = 0; i < m; i++) { 217 | for (j = 0; j < q; j++) { 218 | sum1 = 0;sum2 = 0;sum3 = 0;sum4 = 0; 219 | float* index_t1=mat1 + i*n; 220 | float* index_t2=mat2 + j; 221 | for (k = 0; k < M; k+=4) { 222 | sum1 = sum1 + *(index_t1 + k) * *(index_t2 + k*q); //sum = sum + *(mat1 + i*n + k) * *(mat2 + k*q + j); 223 | sum2 = sum2 + *(index_t1 + k+1) * *(index_t2 + (k+1)*q); 224 | sum3 = sum3 + *(index_t1 + k+2) * *(index_t2 + (k+2)*q); 225 | sum4 = sum4 + *(index_t1 + k+3) * *(index_t2 + (k+3)*q); 226 | } 227 | *(result + i*q + j) = sum1 + sum2+sum3+sum4; 228 | } 229 | } 230 | return(0); 231 | } 232 | 233 | int matMul_N( float *mat1, float *mat2, float *result, int m, int n, int q) { 234 | float sum1,sum2,sum3,sum4; 235 | int i,j,k,K; 236 | for (i = 0; i < m; i++) { 237 | for (j = 0; j < q; j++) { 238 | sum1 = 0;sum2 = 0;sum3 = 0;sum4 = 0; 239 | float* index_t1=mat1 + i*n; 240 | float* index_t2=mat2 + j; 241 | for (k = 0; k < N; k+=4) { 242 | sum1 = sum1 + *(index_t1 + k) * *(index_t2 + k*q); //sum = sum + *(mat1 + i*n + k) * *(mat2 + k*q + j); 243 | sum2 = sum2 + *(index_t1 + k+1) * *(index_t2 + (k+1)*q); 244 | sum3 = sum3 + *(index_t1 + k+2) * *(index_t2 + (k+2)*q); 245 | sum4 = sum4 + *(index_t1 + k+3) * *(index_t2 + (k+3)*q); 246 | } 247 | *(result + i*q + j) = sum1+sum2+sum3+sum4; 248 | } 249 | } 250 | return(0); 251 | } 252 | 253 | int transpose(float *mat1, float *mat2, int m, int n) 254 | { 255 | //transposes mat1_m*n which is input to mat2_n*m which is out 256 | // M,N dimentions of matrices 257 | int i,j,k,K; 258 | for (i = 0; i arr[j + 1]) 149 | swap(&arr[j], &arr[j + 1]); 150 | return(0); 151 | } 152 | 153 | 154 | int matMul(float *mat1, float *mat2, float *result, int m, int n, int q) { 155 | //Multiplication for Mat1_(m*n) * Mat2_(n*k) 156 | // M,N and K are dimentions of matrices 157 | // Output is going to sit in the matrix that result represents here 158 | float sum; int i,j,k; 159 | for (i = 0; i < m; i++) { 160 | for (j = 0; j < q; j++) { 161 | sum = 0; 162 | for (k = 0; k < n; k++) { 163 | sum = sum + *(mat1 + i*n + k) * *(mat2 + k*q + j); 164 | } 165 | *(result + i*q + j) = sum; 166 | } 167 | } 168 | return(0); 169 | } 170 | 171 | 172 | 173 | int matSUB_M(float *mat1, float *mat2, float *result, int m, int n) { 174 | //Calculates mat1_m*n - mat2_m*n and reutrns the resultant matrix to result 175 | //Matrices should be the same size 176 | int i,j; 177 | for (i = 0; i < M; i++) { 178 | for (j = 0; j < n; j++) 179 | *(result + i*n + j) = *(mat1 + i*n + j) - *(mat2 + i*n + j); 180 | } 181 | return(0); 182 | } 183 | 184 | int matADD_N(float *mat1, float *mat2, float *result, int m, int n) { 185 | //Calculates mat1_m*n + mat2_m*n and reutrns the resultant matrix to result 186 | //Matrices should be the same size 187 | int i,j; 188 | for (i = 0; i < N; i++) { 189 | for (j = 0; j < n; j++) 190 | *(result + i*n + j) = *(mat1 + i*n + j) + *(mat2 + i*n + j); 191 | } 192 | return(0); 193 | } 194 | 195 | int transpose(float *mat1, float *mat2, int m, int n) 196 | { 197 | //transposes mat1_m*n which is input to mat2_n*m which is out 198 | // M,N dimentions of matrices 199 | int i,j; 200 | for (i = 0; i 12 | #include "math.h" 13 | 14 | #define M 64 // Number of measurements 15 | #define N 256//Number of samples 16 | #define number_of_finded_Elements 15 17 | #define S 6 //Sparsity degree 18 | #define number_of_iterations 10 19 | 20 | 21 | int number_of_finded = 0; 22 | 23 | int matMul(float *mat1, float *mat2, float *result, int m, int n, int q); 24 | int matMul_M(float *mat1, float *mat2, float *result, int m, int n, int q); 25 | int matMul_N(float *mat1, float *mat2, float *result, int m, int n, int q); 26 | int transpose(float *mat1, float *mat2, int m, int n); 27 | float innerMulColumn_N(float *mat1, float *vector, int numberof_of_rows_Mat1, int numberof_of_columns_Mat1, int C); 28 | int matSUB(float *mat1, float *mat2, float *result, int m, int n); 29 | int matADD(float *mat1, float *mat2, float *result, int m, int n); 30 | int QR(float *A, float *Q, float *R, int n); 31 | int swap(int *xp, int *yp); 32 | int bubbleSort(int *arr, int n); 33 | int print(float *mat, int m, int n); 34 | float sum_array(float *arr, int m); 35 | float innerMatColumnMAT(float *mat, int n, int C1, int C2); 36 | int Union(int *vec, int newval); 37 | int backsubstitotion(float *R, float *y_Qt, float *x_hat, int n); 38 | float norm_Col(float *A, int m, int n, int C); 39 | int max_index(float *vector, int size); 40 | int find_max_index(float *A, float *r, int m, int n, int *finded_index, int *remaining_index, int number_of_remaining, int number_of_finded); 41 | float SNR(float *a, float *b, int Length); 42 | float MSE(float *a, float *b, int Length); 43 | 44 | 45 | static struct timeval tm1; 46 | static inline void start() 47 | { 48 | gettimeofday(&tm1, NULL); 49 | } 50 | 51 | static inline void stop() 52 | { 53 | struct timeval tm2; 54 | gettimeofday(&tm2, NULL); 55 | 56 | unsigned long long t = 1000 * (tm2.tv_sec - tm1.tv_sec) + (tm2.tv_usec - tm1.tv_usec) / 1000; 57 | printf("%llu ms\n", t); 58 | } 59 | 60 | int main() { 61 | 62 | float A[M][N]; 63 | int i,j; 64 | for (i = 0; i < M; i++) 65 | for ( j = 0; j < N; j++){ 66 | A[i][j] =(float)(rand()%10); 67 | } 68 | float x[N]; 69 | float y[M]; 70 | float x_hat[N]; 71 | 72 | /* for (int i = 0;i < M;i++) 73 | for (int j = 0;j < N/4;j=j+4) 74 | { 75 | int data; 76 | _TCE_STREAM_IN("fifo_s16_stream_in_fifo_s16_stream_in_status", data ); 77 | A[i][j]=(float)data; 78 | _TCE_STREAM_IN("fifo_s16_stream_in_fifo_s16_stream_in_status", data ); 79 | A[i][j+1]=(float)data; 80 | _TCE_STREAM_IN("fifo_s16_stream_in_fifo_s16_stream_in_status", data ); 81 | A[i][j+2]=(float)data; 82 | _TCE_STREAM_IN("fifo_s16_stream_in_fifo_s16_stream_in_status", data ); 83 | A[i][j+3]=(float)data; 84 | }*/ 85 | 86 | /* 87 | for (int i = 0; i < M; i++) // WHEN I USE this part all programs inlcuding this one behave strangely!!!!!!!! 88 | for (int j = 0; j < N; j++) 89 | A[i][j] = (2*(rand() % 2)-1) ; 90 | */ 91 | 92 | for (i = 0;i max) 307 | { 308 | max = *(vector + i); 309 | index_of_largest_valyue = i; 310 | } 311 | } 312 | return(index_of_largest_valyue); 313 | } 314 | int QR(float *A, float *Q, float *R, int n) { 315 | 316 | /*Q=A; 317 | 318 | Q(:,1) = Q(:,1); 319 | R(1,1) = norm(Q(:,1)); 320 | Q(:,1) = Q(:,1)/R(1,1); 321 | 322 | for k = 2:n, 323 | R(1:k-1,k) = Q(:,1:k-1)'*Q(:,k); 324 | Q(:,k) = Q(:,k)- Q(:,1:k-1)*R(1:k-1,k); 325 | R(k,k) = norm(Q(:,k)); 326 | Q(:,k) = Q(:,k)/R(k,k); 327 | end 328 | end 329 | */ 330 | int i,j,K; 331 | for ( i = 0;i < n;i++) //Q = A; 332 | for ( j = 0;j < n;j++) { 333 | *(Q + i*n + j) = *(A + i*n + j); 334 | *(R + i*n + j) = 1e-20; 335 | } 336 | /* R(1:k-1, k) = Q(1..n, 1 : k-1)'*Q(1..n,k); 337 | Q(1..n, k) = Q(1..n, k) - Q(1..n, 1 : k-1)*R(1:k-1,k); 338 | R(k, k) = norm(Q(1..n, k)); 339 | Q(1..n, k) = Q(1..n, k) / R(k, k); 340 | */ 341 | for ( K = 0;K < n;K++) { 342 | for ( i = 0;i < K;i++) 343 | *(R + i*n + K) = innerMatColumnMAT(Q, n, i, K); // R(1:k-1,k) = Q(:,1:k-1)'*Q(:,k); 344 | 345 | for ( i = 0;i < n;i++) { 346 | float QinR = 0; 347 | for ( j = 0;j < K;j++) 348 | QinR = QinR + *(Q + i*n + j) * *(R + j*n + K); 349 | *(Q + i*n + K) = *(Q + i*n + K) - QinR; 350 | } 351 | *(R + K*n + K) = norm_Col(Q, n, n, K); 352 | for ( i = 0;i < n;i++) { 353 | 354 | *(Q + i*n + K) = *(Q + i*n + K) / *(R + K*n + K); 355 | } 356 | } 357 | 358 | 359 | 360 | return(1); 361 | } 362 | int matSUB(float *mat1, float *mat2, float *result, int m, int n) { 363 | //Calculates mat1_m*n - mat2_m*n and reutrns the resultant matrix to result 364 | //Matrices should be the same size 365 | int i,j; 366 | for ( i = 0;i < m;i++) { 367 | for ( j = 0;j < n;j++) 368 | *(result + i*n + j) = *(mat1 + i*n + j) - *(mat2 + i*n + j); 369 | } 370 | return(0); 371 | } 372 | 373 | 374 | int matADD(float *mat1, float *mat2, float *result, int m, int n) { 375 | //Calculates mat1_m*n + mat2_m*n and reutrns the resultant matrix to result 376 | //Matrices should be the same size 377 | int i,j; 378 | for ( i = 0;i < m;i++) { 379 | for ( j = 0;j < n;j++) 380 | *(result + i*n + j) = *(mat1 + i*n + j) + *(mat2 + i*n + j); 381 | } 382 | return(0); 383 | } 384 | 385 | 386 | int print(float *mat, int m, int n) { 387 | // Prints mat with dimentions of m and n 388 | int i,j; 389 | for ( i = 0; i < m; i++) { 390 | for ( j = 0; j < n; j++) { 391 | //_TCE_STREAM_OUT((char) *(mat+i*n+j)); 392 | printf("%d ", (int) *(mat + i*n + j)); 393 | } 394 | printf("\n"); 395 | } 396 | return(1); 397 | } 398 | /* 399 | int print_int(int *mat, int m, int n) { 400 | // Prints mat with dimentions of m and n 401 | for (int i = 0;i < m;i++) { 402 | for (int j = 0;j < n;j++) 403 | std::cout << *(mat + i*n + j) << " "; 404 | std::cout << std::endl; 405 | } 406 | return(1); 407 | }*/ 408 | float norm_Col(float *A, int m, int n, int C) 409 | { 410 | int i; 411 | float sum = 0; 412 | float *fixed_part_of_addrss=A + C ; 413 | for ( i = 0;i < m;i++) 414 | sum = sum + *(fixed_part_of_addrss + i*n ) * *(fixed_part_of_addrss + i*n); 415 | sum=sqrt(sum); 416 | return sum; 417 | } 418 | int swap(int *xp, int *yp) 419 | { 420 | int temp = *xp; 421 | *xp = *yp; 422 | *yp = temp; 423 | return(0); 424 | } 425 | int bubbleSort(int *arr, int n) 426 | { 427 | int i, j; 428 | for (i = 0; i < n - 1; i++) 429 | 430 | // Last i elements are already in place 431 | for (j = 0; j < n - i - 1; j++) 432 | if (arr[j] > arr[j + 1]) 433 | swap(&arr[j], &arr[j + 1]); 434 | return(0); 435 | } 436 | int backsubstitotion(float *R, float *y_Qt, float *x_hat, int n) { 437 | int i,j,d; 438 | for ( d = 0;d < n;d++) 439 | *(x_hat + d) = 0; 440 | for ( i = n - 1;i >= 0;i--) 441 | { 442 | *(x_hat + i) = *(y_Qt + i) / *(R + i*n + i); 443 | for ( j = 0;j < i;j++) 444 | *(y_Qt + j) = *(y_Qt + j) - *(R + j*n + i) * *(x_hat + i); 445 | } 446 | return(1); 447 | } 448 | float innerMatColumnMAT(float *mat, int n, int C1, int C2) 449 | {// n is size, C1 and C2 are columns that are correlated 450 | float sum = 0; 451 | int i; 452 | for ( i = 0;i < n;i++) 453 | sum += *(mat + i*n + C1) * *(mat + i*n + C2); 454 | return(sum); 455 | } 456 | int Union(int *vec, int newval) { 457 | // Using this function values of index are sorted and there is no need to check for repitition 458 | int i; 459 | for ( i = 0;i arr[j + 1]) 122 | swap(&arr[j], &arr[j + 1]); 123 | return(0); 124 | } 125 | int backsubstitotion(float *R, float *y_Qt, float *x_hat, int n) { 126 | int i,j,d; 127 | for ( d = 0;d < n;d++) 128 | *(x_hat + d) = 0; 129 | for ( i = n - 1;i >= 0;i--) 130 | { 131 | *(x_hat + i) = *(y_Qt + i) / *(R + i*n + i); 132 | for ( j = 0;j < i;j++) 133 | *(y_Qt + j) = *(y_Qt + j) - *(R + j*n + i) * *(x_hat + i); 134 | } 135 | return(1); 136 | } 137 | float innerMatColumnMAT(float *mat, int n, int C1, int C2) 138 | {// n is size, C1 and C2 are columns that are correlated 139 | float sum = 0; 140 | int i; 141 | for ( i = 0;i < n;i++) 142 | sum += *(mat + i*n + C1) * *(mat + i*n + C2); 143 | return(sum); 144 | } 145 | int Union(int *vec, int newval) { 146 | // Using this function values of index are sorted and there is no need to check for repitition 147 | int i; 148 | for ( i = 0;i 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. 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If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /MATLAB/AMP.m: -------------------------------------------------------------------------------- 1 | function xhat=AMP(y,H,landa,iterAMP,m,n) 2 | %% y is measurement vector; H is measurement matrix, iterAMP is number of iterations, m and n are matrix dimentions 3 | r=y; 4 | s=zeros(n,1); 5 | sqM=sqrt(m); 6 | 7 | for t=1:iterAMP 8 | 9 | maxs=sort(abs(r),'descend'); 10 | sigma=mean(maxs(1:20));%norm(r)/sqM; 11 | g=H'*r; 12 | s=s+g; 13 | 14 | %minOFmaxs=mean(maxs(1:10)); 15 | for i=1:n 16 | s(i)=sign(s(i))*max(abs(s(i))-sigma,0); 17 | end 18 | %for i=1:n %thresholding 19 | % a=middle(i); 20 | % s(i)=sign(a)*max(abs(a)-sigma,0); 21 | %end 22 | b=sum(abs(s)>0)/m; 23 | r=y-H*s+b.*r; 24 | end 25 | xhat=s; 26 | end 27 | -------------------------------------------------------------------------------- /MATLAB/IHT_Mine.m: -------------------------------------------------------------------------------- 1 | function x=IHT_Mine(y,A,k,iteration) 2 | [M,N]=size(A); 3 | xnew=zeros(N,1); 4 | r=y-A*xnew; 5 | for i=1:iteration 6 | g=A'*(r); 7 | w=0.001;%(g'*g)/(g'*(A'*A)*g); 8 | x=xnew+w*g; 9 | [v,s]=sort(abs(x),'descend'); 10 | T=s(1:k); 11 | xnew(:)=0; 12 | xnew(T)=x(T); 13 | r=y-A*xnew; 14 | end 15 | x=xnew; 16 | end 17 | -------------------------------------------------------------------------------- /MATLAB/OMP.m: -------------------------------------------------------------------------------- 1 | function [ s_hat ] = OMP(x,A,q) 2 | [N,K] = size(A); 3 | s_hat= zeros(K,1); 4 | r=x; 5 | T=[]; 6 | for i=1:K 7 | norms(i)=norm(A(:,i)); 8 | end 9 | for ii = 1:q 10 | g= A'*r; 11 | for b3=1:K 12 | f(b3)=abs(g(b3))/norms(b3); 13 | end 14 | jj = find(f == max(f)); 15 | T = union(T,jj); 16 | s_hat(T)=pinv(A(:,T)) * x; %%coeffecient update 17 | r=x-A*s_hat; %%residu update 18 | if (mse(x,s_hat) < .1) 19 | break; 20 | end 21 | end 22 | 23 | 24 | 25 | -------------------------------------------------------------------------------- /MATLAB/readme.md: -------------------------------------------------------------------------------- 1 | Here are MATLAB footprint implementation of compressive sensing recovery algorithms. The AMP initial coefficient are taken from Baranuik's work for fast convergence. 2 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | Three well-known Sparse Recovery Algorithms implemented in C/C++ and MATLAB: 2 | 3 | 4 | I. Orthogonal Matching Pursuit ( OMP ), 5 | II. Iterative Hard Thresholding ( IHT ), 6 | III. Approximage Message Passing ( AMP ) 7 | Notice AMP needs intitial coefficients that were taken from Baranuik's work (detail in the code). Further the C code contains all subroutins that includes: QR decompostion, Gausian elimination, bubble-sort, back-substitution, etc. 8 | Matrix multipications, correlation computations 9 | SNR, MSE 10 | 11 | # Introduction 12 | Excerpts are from our paper [1]. 13 | 14 | OMP is a greedy algorithm introduced as an extension to the well-established 15 | Matching Pursuit algorithm. The OMP algorithm iteratively finds the best matrix 16 | columns that correspond to the non-zero coefficients of the sparse signal, and then 17 | performs a least squares (LS) optimization in the subspace formed from current and 18 | previously selected columns. AMP and the IHT algorithms do not require LS in each 19 | iteration, and instead perform simple vector truncation, which results in an 20 | iterative completion of the sparse signal. The parameters, such as step size and 21 | threshold, are critical in the performance of AMP and IHT algorithms. The optimum 22 | parameters of AMP are chosen based on the experimental results of . In the case of 23 | the IHT algorithm, a different flavor of algorithm called Normalized-IHT was 24 | implemented, where the step size is automatically determined in each iteration. 25 | 26 | 27 | # Results 28 | 29 | For fair comparison of the algorithms, one must take into consideration the window 30 | length of the signal, the sparsity degree of the test signal, the hyperparameters 31 | of the algorithms, such as termination criteria and desired reconstruction quality. 32 | From Fig. 4 [following figure], we observed that the OMP algorithm is fastest in 33 | reconstruction, whereas the AMP and IHT algorithms that are known to be computationally 34 | cheaper, appear to be slower. 35 | 36 | ![alt text]( https://github.com/NeuroFan/Compressive_Sensing/blob/master/performance_comparison.png) 37 | 38 | 39 | This is due to the low sparsity degree and short signal length. The OMP algorithm gives 40 | better performance for less sparse signals [27], and here the experiments were done 41 | with signals with less than 10% occupancy. The IHT algorithm’s performance is relatively 42 | independent from the sparsity degree, and the performance of AMP is less sensitive to 43 | sparsity degree than the OMP,. These issues are rather strong practical arguments for 44 | flexible designs. 45 | 46 | 47 | # Citation 48 | 49 | If you used the code please cite our paper [1]. 50 | 51 | You can find the paper in this repository or through following link: 52 | https://github.com/NeuroFan/Compressive_Sensing/blob/master/An%20Embedded%20Programmable%20Processor%20for%20Compressive.pdf 53 | 54 | *Reference* 55 | 56 | [1] M. Safarpour, I. Hautala and O. Silvén, "An Embedded Programmable Processor for Compressive Sensing Applications," 2018 IEEE Nordic Circuits and Systems Conference (NORCAS): NORCHIP and International Symposium of System-on-Chip (SoC), Tallinn, Estonia, 2018, pp. 1-5. 57 | 58 | doi: 10.1109/NORCHIP.2018.8573494 59 | -------------------------------------------------------------------------------- /performance_comparison.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/NeuroFan/Compressive_Sensing_C_and_MATLAB/fc90eaaef090bc1a9cfa2698191c682425785998/performance_comparison.png --------------------------------------------------------------------------------