Update FAR vs PD

FAR vs PD/FAR_simu.m

@@ -1,4 +1,4 @@
-function P_fa = FAR_simu(threshold)
+function threshold = FAR_simu(P_fa_FAR)
     global N M epi trail_times
 
     % Define measurement matrix
@@ -9,64 +9,124 @@ function P_fa = FAR_simu(threshold)
     Lambda_C = setdiff(1:N*M, Lambda);
 
     % Try "trail_times" times
-    NN = N;
+    results_0 = zeros(trail_times, N * M);
-    results = zeros(trail_times, N * M);
+    results_1 = zeros(trail_times, N * M);
-
+    thresholds_0 = [];
-    if exist("FAR_recovery_1_LASSO_5.mat")
+    thresholds_1 = [];
-        load("FAR_recovery_0_debiasedLASSO_500.mat", "results");
+    
+    noise_sigma = 0.01;
+    noise_sigma_2 = noise_sigma ^ 2;
+    
+    if exist("520BP.mat")
+        load("50.mat", "results_0", "results_1");
     else
+        % 0 假设
         for T = 1: trail_times
             % y = Ax + n
-            n = randn(NN, 1) * 0.1;
+            n = randn(N, 1) * noise_sigma;
+            y_noise = n;
+            [x_hat, threshold] = debiased_LASSO(A, y_noise, P_fa_FAR, noise_sigma_2);
+            results_0(T, :) = x_hat;
+            thresholds_0 = [thresholds_0 threshold];
+        end
+        % 1 假设
+        for T = 1: trail_times
+            % y = Ax + n
+            n = randn(N, 1) * noise_sigma;
             y_noise = A * x + n;
-            
+            [x_hat, threshold] = debiased_LASSO(A, y_noise, P_fa_FAR, noise_sigma_2);
-            % x_hat = CS(A, y)
+            results_1(T, :) = x_hat;
-            x_hat = recovery(A, y_noise);
+            thresholds_1 = [thresholds_1 threshold];
-            results(T, :) = x_hat;
         end
     end
 
     % Distribute of H_0 and H_1
-    H_0_distribute = zeros(1, length(Lambda_C));
+    H_00_distribute = zeros(1, length(Lambda_C));
-    H_1_distribute = zeros(1, length(Lambda));
+    H_01_distribute = zeros(1, length(Lambda));
+    H_10_distribute = zeros(1, length(Lambda_C));
+    H_11_distribute = zeros(1, length(Lambda));
 
     i1 = 1;
     i2 = 1;
-    Ts = [];
+    T_00 = [];
+    T_01 = [];
+    T_10 = [];
+    T_11 = [];
     
-    for t = 1: trail_times
+    for threshold = 1: trail_times
-        x_hat = results(t, :);
+        x_0_hat = results_0(threshold, :);
-        T = 0;
+        x_1_hat = results_1(threshold, :);
+        t_00 = 0;
+        t_01 = 0;
+        t_10 = 0;
+        t_11 = 0;
+
         for i = 1: length(x)
             if ismember(i, Lambda_C)
-                H_0_distribute(i1) = x_hat(i);
+                t_00 = t_00 + abs(x_0_hat(i));
+                t_10 = t_10 + abs(x_1_hat(i));
+                H_00_distribute(i1) = x_0_hat(i);
+                H_10_distribute(i1) = x_1_hat(i);
                 i1 = i1 + 1;
             elseif ismember(i, Lambda)
-                T = T + abs(x_hat(i));
+                t_01 = t_01 + abs(x_0_hat(i));
-                H_1_distribute(i2) = x_hat(i);
+                t_11 = t_11 + abs(x_1_hat(i));
+                H_01_distribute(i2) = x_0_hat(i);
+                H_11_distribute(i2) = x_1_hat(i);
                 i2 = i2 + 1;
             end
         end
-        Ts = [Ts T];
+        T_00 = [T_00 t_00];
+        T_01 = [T_01 t_01];
+        T_10 = [T_10 t_10];
+        T_11 = [T_11 t_11];
     end
 
 
     % Draw
     figure(1)
-    subplot(2, 1, 1);
+    subplot(2, 2, 1);
     title("Freq histogram of H_0");
-    histfit(real(H_0_distribute));
+    histfit(real(H_00_distribute));
     
-    subplot(2, 1, 2);
+    subplot(2, 2, 2);
     title("Freq histogram of H_1");
-    histfit(real(H_1_distribute));
+    histfit(real(H_01_distribute));
+
+    subplot(2, 2, 3);
+    title("Freq histogram of H_0");
+    histfit(real(H_10_distribute));
     
-    H_0_mean = mean(H_0_distribute);
+    subplot(2, 2, 4);
-    H_0_std = std(H_0_distribute);
+    title("Freq histogram of H_1");
-    H_1_mean = mean(H_1_distribute);
+    histfit(real(H_11_distribute));
-    H_1_std = std(H_1_distribute);
+    
+    H_00_mean = mean(H_00_distribute);
+    H_00_std = std(H_00_distribute);
+    H_01_mean = mean(H_01_distribute);
+    H_01_std = std(H_01_distribute);
+    H_10_mean = mean(H_10_distribute);
+    H_10_std = std(H_10_distribute);
+    H_11_mean = mean(H_11_distribute);
+    H_11_std = std(H_11_distribute);
+
+    fprintf("H_00: mu = %f, std = %f\n", H_00_mean, H_00_std);
+    fprintf("H_01: mu = %f, std = %f\n", H_01_mean, H_01_std);
+    fprintf("H_10: mu = %f, std = %f\n", H_10_mean, H_10_std);
+    fprintf("H_11: mu = %f, std = %f\n", H_11_mean, H_11_std);
+
+    figure(2);
+    subplot(2, 2, 1);
+    histfit(real(T_00));
+    
+    subplot(2, 2, 2);
+    histfit(real(T_01));
+
+    subplot(2, 2, 3);
+    histfit(real(T_10));
+    
+    subplot(2, 2, 4);
+    histfit(real(T_11));
 
-    fprintf("H_0: mu = %f, std = %f\n", H_0_mean, H_0_std);
-    fprintf("H_1: mu = %f, std = %f\n", H_1_mean, H_1_std);
     % P_fa = normcdf(threshold, H_0_mean, H_0_std);
 end

FAR vs PD/Main.m

@@ -7,19 +7,20 @@ N = 64;
 M = 4;
 K = 10;
 lambda = zeros(M * N, 1);
-lambda(:) = 0.3;
+lambda(:) = 0.8;
-tau = 1e-4;
+tau = 1e-6;
-iter_max = 500;
+iter_max = 50;
-% method = "debiased_LASSO";
+method = "debiased_LASSO";
 % method = "LASSO";
-method = "BP";
+% method = "BP";
 % method = "VAMP";
-trail_times = 1e2;
+trail_times = 1000;
 epi = 0;
 extend_target = 1;
 
 %% FAR
-P_fa_FAR = FAR_simu(3);
+P_fa_FAR = 1e-5;
+threshold_FAR = FAR_simu(P_fa_FAR);
 % fprintf("FAR: %f\n", P_fa_FAR);
 
 %% PD

FAR vs PD/check_orth.m

@@ -0,0 +1,25 @@
+clc; clear;
+N = 16;
+M = 4;
+epi = 0;
+
+d_n = floor(rand(N, 1)*M) / M;
+A = get_Psi(N, M, d_n, epi);
+B = get_Psi_2(N, M, d_n, epi);
+C = A - B;
+real_C = real(C);
+imag_C = imag(C);
+
+% subplot(121)
+% heatmap(real_C)
+% 
+% subplot(122)
+% heatmap(imag_C)
+
+r = zeros(N);
+for i = 1: N
+    for j = 1: N
+        r(i, j) = A(i, :) * (A(j, :)');
+    end
+end
+heatmap(abs(r));

FAR vs PD/recovery.m

@@ -25,6 +25,14 @@ function x_hat = recovery(A, y_noise)
         x_d_CROD = x_LASSO + A'*(y_noise - A*x_LASSO)/Q_hat;
         x_hat = x_d_CROD;
 
+        RSS = 1/sz(2) * norm(y_noise - A * x_LASSO, 2)^2;
+        noise_sigma_2 = 1e-4;
+        P_fa = normcdf(1, 0, 1);
+        sigma_w_2 = (gamma * (1-gamma)) / ((gamma - Rho)^2) * RSS + noise_sigma_2;
+        k_d = -sigma_w_2 * log(P_fa);
+
+        fprintf("%f %f %f\n", gamma, sigma_w_2, k_d);
+
     elseif method == "LASSO"
         sz = size(A);
         N = sz(2);
@@ -47,7 +55,7 @@ function x_hat = recovery(A, y_noise)
         cvx_end
     else
         global lambda tau iter_max;
-        [x_hat, z_hat_d] = cVAMPro(y_noise, A, lambda, tau, iter_max);
+        [x_hat, x_hat_d] = cVAMPro(y_noise, A, lambda, tau, iter_max);
     end
 end