0001
0002
0003
0004
0005
0006
0007 clc;
0008 clear;
0009
0010
0011 addpath misc/
0012 addpath prox_operators/
0013
0014
0015 N = 64;
0016 input_snr = 30;
0017 randn('seed', 1); rand('seed', 1);
0018
0019
0020 im = zeros(N); ind = randperm(N^2); im(ind(1:100)) = 1;
0021
0022 figure(1);
0023 subplot(221), imagesc(im); axis image; axis off;
0024 colormap gray; title('Original image'); drawnow;
0025
0026
0027
0028 mask = rand(size(im)) < 0.095; ind = find(mask==1);
0029
0030 Ma = sparse(1:numel(ind), ind, ones(numel(ind), 1), numel(ind), numel(im));
0031
0032 A = @(x) Ma*x(:);
0033 At = @(x) reshape(Ma'*x(:), size(im));
0034
0035
0036
0037
0038 A = @(x) Ma*reshape(fft2(x)/sqrt(numel(im)), numel(x), 1);
0039 At = @(x) ifft2(reshape(Ma'*x(:), size(im))*sqrt(numel(im)));
0040
0041
0042 Psit = @(x) x; Psi = Psit;
0043
0044
0045 y = A(im);
0046
0047
0048 sigma_noise = 10^(-input_snr/20)*std(im(:));
0049 y = y + (randn(size(y)) + 1i*randn(size(y)))*sigma_noise/sqrt(2);
0050
0051
0052 figure(1);
0053 subplot(222); imagesc(real(At(y))); axis image; axis off;
0054 colormap gray; title('Measured image'); drawnow;
0055
0056
0057 epsilon = sqrt(chi2inv(0.99, 2*numel(ind))/2)*sigma_noise;
0058
0059
0060 param.verbose = 1;
0061 param.gamma = 1e-1;
0062 param.rel_obj = 1e-4;
0063 param.max_iter = 300;
0064 param.nu_B2 = 1;
0065 param.tol_B2 = 1e-4;
0066 param.tight_B2 = 1;
0067 param.tight_L1 = 1;
0068 param.pos_l1 = 1;
0069
0070
0071 sol = sopt_mltb_solve_BPDN(y, epsilon, A, At, Psi, Psit, param);
0072
0073
0074 figure(1);
0075 subplot(223); imagesc(real(sol)); axis image; axis off;
0076 colormap gray; title(['First estimate - ', ...
0077 num2str(sopt_mltb_SNR(im, real(sol))), 'dB']); drawnow;
0078
0079
0080 param.weights = 1./(abs(sol)+1e-5);
0081 sol = sopt_mltb_solve_BPDN(y, epsilon, A, At, Psi, Psit, param);
0082
0083
0084 figure(1);
0085 subplot(224); imagesc(real(sol)); axis image; axis off;
0086 colormap gray; title(['Second estimate - ', ...
0087 num2str(sopt_mltb_SNR(im, real(sol))), 'dB']); drawnow;