Add Example

2024-11-11 16:32:53 +08:00
parent a2cb6d1825
commit 29ae9585f9
56 changed files with 4029 additions and 0 deletions
@@ -0,0 +1,57 @@
+function [ x_mf_norm, x_cs_norm ] = yAxn_recovery( A, SNR, Target_index, lambda )
+
+    % matrix parameters
+    [M, N] = size(A);
+    mul = A(:,1)'*A(:,1);
+    
+    % H0 sample
+    L = round(Target_index + N * 0.1);
+    R = round(N * 0.9);
+    Lambda_C = L: R;
+    
+    % parameters
+    sigma_n = 0.1;
+    Target_amplitude = sqrt(10^(SNR/10) * sigma_n^2 / mul);
+
+    
+    %% CS setting
+    % CS-parameters
+%     lambda = 0.0005;
+    alpha = 1/4;
+    delta = 1e-8*alpha;
+    
+    % CS-normalization
+    J1 = A*A';
+    lambda_J=eig(J1);
+    A_norm = A / sqrt(lambda_J(end));
+    Hp = A_norm'*A_norm;
+    [~, D] = eig(Hp);
+    d = diag(D);
+    sigma_n_norm = sigma_n / sqrt(lambda_J(end));
+    
+    
+    %% generate x
+    x = zeros(N, 1);
+    x(Target_index) = Target_amplitude;
+    
+    
+    %% generate y
+    noise = random('Normal', 0, sigma_n/sqrt(2), M, 1) + 1j * random('Normal', 0, sigma_n/sqrt(2), M, 1);
+    y = A*x + noise;
+    
+    
+    %% recover
+    % MF
+    x_mf = A' * y ./ mul;
+    sigma_MF = sqrt(var(x_mf(Lambda_C)));
+    x_mf_norm = x_mf ./ sigma_MF;
+    
+    % CS
+    y_norm = y / sqrt(lambda_J(end));
+    x_FISTA = FISTA_v1(y_norm, A_norm, lambda, delta, Hp);
+    [x_d_cal_f, hat_Q1_cal_f, sigma_d_cal_f] = cal_debiased_LASSO_v1(x_FISTA, A_norm, y_norm, lambda, sigma_n_norm, d);
+    sigma_CS = sqrt(var(x_d_cal_f(Lambda_C)));
+    x_cs_norm = x_d_cal_f ./ sigma_CS;
+    
+end
+