Add Example

0 - example/nsq - 恢复算法/cVAMPa_dampling.m

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+function[x, x_d, hat_Q1, sigma_d, ifcvg] = cVAMPa_dampling(y, A, lambda, alpha, delta, iter_max, sigma)
+
+[M, N] = size(A);
+
+gamma = M/N;
+p = A'*y;
+h1 = p/gamma;
+hat_Q1 = gamma;
+
+%Eigenvalue Decomposition
+[V, D] = eig(A'*A);
+d = diag(D); 
+
+t = 0;
+diff = 1;
+
+while((diff > delta) && (t < iter_max))
+    
+    h1_pre = h1;
+    
+    % Factorized
+    x1 = sft_thd(h1, lambda/hat_Q1);
+    chi1 = sum((abs(x1) > 1e-4).* (2 - lambda./((hat_Q1*abs(x1) + lambda)))) / 2 / N / hat_Q1;
+    % Message F to G
+    hat_Q2 = 1/chi1 - hat_Q1;
+    h2 = (x1/chi1 - h1*hat_Q1)/hat_Q2;
+    % Gaussian
+    tmp = V'*(p + h2*hat_Q2);
+    tmp = tmp./(d+hat_Q2);
+    x2 = V*tmp;
+    chi2 = sum(1./(d+hat_Q2))/N;
+    % Message G to F
+    hat_Q1 = 1/chi2 - hat_Q2;
+    h1 = alpha*(x2/chi2 - h2*hat_Q2)/hat_Q1+(1-alpha)*h1;
+    
+    diff = sum(abs(h1_pre - h1))/sum(abs(h1));
+    t = t+1;
+    
+end
+
+ifcvg = diff <= delta;
+
+x = x1;
+x_d = h1;
+
+chi = chi1;
+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
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