Add basic code

2024-07-16 15:54:44 +08:00
parent 088f1a82fd
commit e98983b374
5 changed files with 65 additions and 43 deletions
@@ -0,0 +1,31 @@
+function [x_hat, threshold] = debiased_LASSO(A, y_noise, P_fa, noise_sigma_2)
+    sz = size(A);
+    N = sz(2);
+    LASSO_lambda = 2;
+
+    gamma = sz(1) / sz(2);
+
+    cvx_begin quiet
+        variable x_LASSO(N) complex
+        minimize(LASSO_lambda * norm(x_LASSO, 1) + norm(y_noise - A * x_LASSO, 2))
+    cvx_end
+
+    rho_active = sum(abs(x_LASSO) > 1e-3)/N;
+    Q_hat = (gamma - rho_active)/(1 - rho_active);
+    Rho = sum((abs(x_LASSO) > 1e-3).* (2 - LASSO_lambda./(Q_hat*abs(x_LASSO) + LASSO_lambda))) / 2 / N;
+    diff = 1;
+    while(diff > 1e-4)
+        Rho_pre = Rho;
+        Rho = sum((abs(x_LASSO) > 1e-3).* (2 - LASSO_lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + LASSO_lambda))) / 2 / N;
+        diff = abs(Rho - Rho_pre);
+    end
+    Q_hat = (gamma-Rho)/(1-Rho);
+    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;
+    sigma_w_2 = (gamma * (1 - gamma)) / ((gamma - Rho)^2) * RSS + noise_sigma_2;
+    threshold = -sigma_w_2 * log(P_fa);
+    
+end
+