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 +1,146 @@
+% echo_mtx: echo data
+% A: chirp matrix
+% sigma_n: input noise standard deviation
+% lambda: LASSO weight
+% delta: convergence normalized difference
+
+% echo_r_mtx: range processing echo data
+% signal_n_o: output noise standard deviation
+
+
+function [ echo_r_mtx, sigma_n_o ] = range_process_CS(echo_mtx, A, sigma_n, lambda, delta)
+
+    % parameters
+    if nargin < 5
+        delta = 2e-7;
+    end
+    [M, N] = size(A);
+    [lenA, M, lenP] = size(echo_mtx);
+    
+    % normalization
+    J1 = A*A';
+    lambda_J=eig(J1);
+    A = A / sqrt(lambda_J(end));
+    echo_mtx = echo_mtx ./ sqrt(lambda_J(end));
+    sigma_n = sigma_n / sqrt(lambda_J(end));
+    
+    % compressed sensing
+    echo_r_mtx = zeros(lenA, N, lenP);
+    for numA = 1: lenA
+        for numP = 1: lenP
+            sr = echo_mtx(numA, :, numP);
+            y = transpose(sr);
+            % LASSO
+            x_FISTA = FISTA(y, A, lambda, delta);
+            % debiased LASSO
+            [x_d, sigma_w] = cal_debiased_LASSO(x_FISTA, A, y, lambda, sigma_n);
+            echo_r_mtx(numA, :, numP) = x_d;
+        end
+    end
+    
+    % calculate output noise
+    sigma_n_o = sigma_w;
+    
+end
+
+
+% algorithm for LASSO
+% y: measurements
+% A: measurement matrix
+% lambda: LASSO weight
+% delta: convergence normalized difference
+% z: LASSO estimator
+function [z] = FISTA(y, A, lambda, delta)
+
+    x_pre = A'*y;
+    t = 1;
+    z = x_pre;
+    z_pre = z;
+    t_pre = t;
+    N = size(A, 2);
+    diff = 1;
+    E = eig(A'*A);
+    L = E(end);
+    temp1 = A'*y/L;
+    temp2 = eye(N) - A'*A/L;
+    k = 0;
+    
+    while((diff > delta) && (k < 1000))
+        temp = temp1 + temp2 * z_pre;
+        x = sft_thd(temp, lambda/L);
+        t = 0.5*(1 + sqrt(1+4*t_pre*t_pre));
+        z = x + (x - x_pre) * (t_pre-1) / t;
+        diff = mean(abs(z_pre - z)); 
+        x_pre = x;
+        z_pre = z;
+        t_pre = t;
+        k = k + 1;
+    end
+
+end
+
+
+% soft threshold function
+% x: processing object
+% thd: threshold
+% y: result
+function y = sft_thd(x, thd)
+
+    if isequal(size(x), size(thd))
+        tmp = abs(x);
+        y = x;
+        y(tmp <= thd) = 0;
+        y(tmp > thd) = (tmp(tmp > thd) - thd(tmp > thd)) .* x(tmp > thd) ./ tmp(tmp > thd);
+    else
+        tmp = abs(x);
+        y = x;
+        y(tmp <= thd) = 0;
+        y(tmp > thd) = (tmp(tmp > thd) - thd) .* x(tmp > thd) ./ tmp(tmp > thd);
+    end
+
+end
+
+
+% calculate debiased LASSO estimator
+% x: LASSO estimator
+% A: measurement matrix
+% y: measurements
+% lambda: LASSO weight
+% sigma_n: input noise standard deviation
+% x_d: debiased LASSO estimator
+% sigma_d: equivalent noise standard deviation
+function [x_d, sigma_d] = cal_debiased_LASSO(x, A, y, lambda, sigma)
+
+    [M, N] = size(A);
+    gamma = M/N;
+    hat_Q1 = gamma;
+    [~, D] = eig(A'*A);
+    d = diag(D);
+
+    diff = 1;
+    T = 1000;
+    t = 0;
+
+    while (t < T) && (diff > 1e-6)
+        Q1_pre = hat_Q1;
+        rho = mean((2 - lambda./(hat_Q1*abs(x) + lambda)).*(abs(x) > 1e-4))/2;
+        hat_Q1 = rho/mean(1./(d + (1-rho)*hat_Q1/rho));
+        diff = abs(Q1_pre - hat_Q1);
+        t = t+1;
+    end
+
+    x_d = x + 1/hat_Q1*A'*(y - A*x);
+
+    chi = rho/hat_Q1;
+    hat_Q2 = 1/chi - hat_Q1;
+
+    t = -hat_Q2;
+    t_prime = -1/mean((1./(d+hat_Q2)).^2);
+    G_prime = t + 1/chi;
+    G_wprime = t_prime + 1/chi/chi;
+    RSS = sum(abs(y - A*x).^2)/M;
+    hat_chi = gamma*G_wprime/(2*G_prime-2*chi*G_wprime)*RSS +...
+        (-G_wprime*gamma+G_prime*G_prime)/(2*G_prime-2*chi*G_wprime)*sigma^2;
+    sigma_d = sqrt(2*hat_chi)/hat_Q1;
+
+end