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0010 clc
0011 clear;
0012
0013
0014
0015
0016 addpath misc/
0017 addpath prox_operators/
0018 addpath test_images/
0019
0020
0021
0022
0023
0024 load Brain_low_res
0025 im=abs(map_ref);
0026
0027
0028 im = im/max(max(im));
0029
0030
0031 im(im<0) = 0;
0032
0033
0034
0035 input_snr = 30;
0036
0037
0038
0039
0040
0041 p=0.05;
0042
0043
0044
0045
0046
0047 nlevel=4;
0048
0049 dwtmode('per');
0050 [C,S]=wavedec2(im,nlevel,'db8');
0051 ncoef=length(C);
0052 [C1,S1]=wavedec2(im,nlevel,'db1');
0053 ncoef1=length(C1);
0054 [C2,S2]=wavedec2(im,nlevel,'db2');
0055 ncoef2=length(C2);
0056 [C3,S3]=wavedec2(im,nlevel,'db3');
0057 ncoef3=length(C3);
0058 [C4,S4]=wavedec2(im,nlevel,'db4');
0059 ncoef4=length(C4);
0060 [C5,S5]=wavedec2(im,nlevel,'db5');
0061 ncoef5=length(C5);
0062 [C6,S6]=wavedec2(im,nlevel,'db6');
0063 ncoef6=length(C6);
0064 [C7,S7]=wavedec2(im,nlevel,'db7');
0065 ncoef7=length(C7);
0066
0067
0068
0069 Psit = @(x) [wavedec2(x,nlevel,'db1')'; wavedec2(x,nlevel,'db2')';wavedec2(x,nlevel,'db3')';...
0070 wavedec2(x,nlevel,'db4')'; wavedec2(x,nlevel,'db5')'; wavedec2(x,nlevel,'db6')';...
0071 wavedec2(x,nlevel,'db7')';wavedec2(x,nlevel,'db8')']/sqrt(8);
0072
0073 Psi = @(x) (waverec2(x(1:ncoef1),S1,'db1')+waverec2(x(ncoef1+1:ncoef1+ncoef2),S2,'db2')+...
0074 waverec2(x(ncoef1+ncoef2+1:ncoef1+ncoef2+ncoef3),S3,'db3')+...
0075 waverec2(x(ncoef1+ncoef2+ncoef3+1:ncoef1+ncoef2+ncoef3+ncoef4),S4,'db4')+...
0076 waverec2(x(ncoef1+ncoef2+ncoef3+ncoef4+1:ncoef1+ncoef2+ncoef3+ncoef4+ncoef5),S5,'db5')+...
0077 waverec2(x(ncoef1+ncoef2+ncoef3+ncoef4+ncoef5+1:ncoef1+ncoef2+ncoef3+ncoef4+ncoef5+ncoef6),S6,'db6')+...
0078 waverec2(x(ncoef1+ncoef2+ncoef3+ncoef4+ncoef5+ncoef6+1:ncoef1+ncoef2+ncoef3+ncoef4+ncoef5+ncoef6+ncoef7),S7,'db7')+...
0079 waverec2(x(ncoef1+ncoef2+ncoef3+ncoef4+ncoef5+ncoef6+ncoef7+1:ncoef1+ncoef2+ncoef3+ncoef4+ncoef5+ncoef6+ncoef7+ncoef),S,'db8'))/sqrt(8);
0080
0081
0082 Psit2 = @(x) wavedec2(x, nlevel,'db8');
0083 Psi2 = @(x) waverec2(x,S,'db8');
0084
0085
0086
0087 mask = sopt_mltb_vdsmask(size(im,1),size(im,2),p);
0088 ind = find(mask==1);
0089
0090 Ma = sparse(1:numel(ind), ind, ones(numel(ind), 1), numel(ind), numel(im));
0091
0092
0093
0094
0095 A = @(x) Ma*reshape(fft2(x)/sqrt(numel(ind)), numel(x), 1);
0096 At = @(x) (ifft2(reshape(Ma'*x(:), size(im))*sqrt(numel(ind))));
0097
0098
0099 y = A(im);
0100
0101 sigma_noise = 10^(-input_snr/20)*std(im(:));
0102 y = y + (randn(size(y)) + 1i*randn(size(y)))*sigma_noise/sqrt(2);
0103
0104
0105
0106 epsilon = sqrt(numel(y)+2*sqrt(numel(y)))*sigma_noise;
0107 epsilon_up = sqrt(numel(y)+2.1*sqrt(numel(y)))*sigma_noise;
0108
0109
0110
0111 param.verbose = 1;
0112 param.gamma = 1e-1;
0113 param.rel_obj = 4e-4;
0114 param.max_iter = 200;
0115 param.tol_B2 = 1-(epsilon/epsilon_up);
0116 param.nu_B2 = 1;
0117 param.tight_B2 = 0;
0118 param.pos_B2 = 1;
0119 param.tight_L1 = 1;
0120 param.nu_L1 = 1;
0121 param.max_iter_L1 = 20;
0122 param.rel_obj_L1 = 1e-2;
0123
0124
0125 maxiter=10;
0126 sigma=sigma_noise*sqrt(numel(y)/(numel(im)*9));
0127 tol=1e-3;
0128 sol1 = sopt_mltb_solve_rwBPDN(y, epsilon, A, At, Psi, Psit, param, sigma, tol, maxiter);
0129
0130 RSNR1=20*log10(norm(im,'fro')/norm(im-sol1,'fro'));
0131
0132
0133
0134 param1.verbose = 1;
0135 param1.gamma = 3e-1;
0136 param1.rel_obj = 5e-4;
0137 param1.max_iter = 200;
0138 param1.max_iter_TV = 200;
0139 param1.nu_B2 = 1;
0140 param1.tol_B2 = 1-(epsilon/epsilon_up);
0141 param1.tight_B2 = 0;
0142 param1.max_iter_B2 = 200;
0143 param1.pos_B2 = 1;
0144
0145
0146 sol2 = sopt_mltb_solve_TVDN(y, epsilon, A, At, param1);
0147
0148 RSNR2=20*log10(norm(im,'fro')/norm(im-sol2,'fro'));
0149
0150
0151
0152 sol3 = sopt_mltb_solve_BPDN(y, epsilon, A, At, Psi2, Psit2, param);
0153
0154
0155 RSNR3=20*log10(norm(im,'fro')/norm(im-sol3,'fro'));
0156
0157 figure, imagesc(sol1,[0 1]);axis image;axis off; colormap gray;
0158 title(['SARA, SNR=',num2str(RSNR1), 'dB'])
0159 figure, imagesc(sol2,[0 1]);axis image;axis off; colormap gray;
0160 title(['TV, SNR=',num2str(RSNR2), 'dB'])
0161 figure, imagesc(sol3,[0 1]);axis image;axis off; colormap gray;
0162 title(['BPDb8, SNR=',num2str(RSNR3), 'dB'])
0163 figure, imagesc(im, [0 1]); axis image; axis off; colormap gray;
0164 title('Original image')
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