Add Macroscopic Analysis of VAMP in a MMS folder

Macroscopic Analysis of VAMP in a MMS/cVAMP.m

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+% Input:y,A,lambda,tau,Kit
+% Output:x_hat_wl,x_hat_d
+
+function [x_hat_wl, x_hat_d] = cVAMP(y, A, lambda, tau, Kit)
+    % Initialization
+    gamma = 768 ./ 1024;
+    k = 0;
+    p = ctranspose(A) * y;
+    h_1 = p;
+    Q_1 = gamma;
+    tau_d = 1;
+
+    % while
+    while (k < Kit) && (tau_d > tau)
+        % Factorized Part
+        x_1 = ST(h_1, lambda, Q_1); % \hat{x}_1^{(k)}
+        chi_1 = F1(x_1, lambda, Q_1); % \chi_1^{(k)}
+        % Message Passing
+        h_2 = x_1 ./ chi_1 - h_1; % h_2^{(k)}
+        Q_2 = 1 ./ chi_1 - Q_1; % \hat{Q}_2^{(k)}
+        % Gaussian Part
+        t1 = (p + h_2) ./ Q_2;
+        t2 = ctranspose(A) * (A * (p + h_2)) / ((Q_2 + 1) * Q_2);
+        x_2 = t1 + t2; % \hat{x}_2^{(k)}
+        chi_2 = gamma ./ (Q_2 + 1) + (1 - gamma) ./ Q_2;
+        % Message Passing
+        h_1_next = x_2 ./ chi_2 - h_2;
+        Q_1_next = 1 ./ chi_2 - Q_2;
+        tau_d = norm(h_1_next - h_1) ./ norm(h_1_next);
+        k = k + 1;
+        % output
+        x_hat_wl = x_1;
+        x_hat_d = h_1_next ./ Q_1_next;
+        % next
+        h_1 = h_1_next;
+        Q_1 = Q_1_next;
+    end
+
+end
+
+% SoftThreshold function
+function x = ST(h_1, lambda, Q_1)
+    [N, M] = size(h_1);
+    x = zeros(N, M);
+
+    for i = 1:N
+        % sign = h_1(i) ./ abs(h_1(i));
+        diff = abs(h_1(i)) - lambda(i);
+        x(i) = sign(h_1(i)) .* (diff ./ Q_1) .* SF(diff);
+    end
+
+end
+
+% Heaviside's step function
+function v = SF(a)
+    % if a > 0
+    %     v = 1;
+    % elseif a == 0
+    %     v = 0;  % at zero points
+    % else
+    %     v = 0;
+    % end
+    v = heaviside(a);
+end
+
+% SoftThreshold function
+function v = F1(x_1, lambda, Q_1)
+    [N, M] = size(x_1);
+    count = 0;
+
+    for i = 1:N
+        temp = Q_1 .* abs(x_1(i)) + lambda(i);
+        count = count + (2 - lambda(i) ./ temp) .* SF(abs(x_1(i)));
+    end
+
+    v = count ./ (2 .* N .* Q_1);
+end

Macroscopic Analysis of VAMP in a MMS/demo1.m

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+% Input:y,A,lambda,tau,Kit
+% Output:x_hat_wl,x_hat_d
+clear;
+clc;
+% rng(1); % 随机种子
+
+%% test_稀疏向量
+% 设定稀疏度
+k = 100; % 设定稀疏度
+
+% 构造感知矩阵D
+m = 768; % 感知矩阵行数
+n = 1024; % 感知矩阵列数 （n>>m）
+
+% D = randn(m,n);     % 生成满足高斯分布的感知矩阵 64*256
+
+F = dftmtx(n);
+row_indices = randperm(n, m);
+D = F(row_indices, :);
+
+% 构造稀疏信号X——共n个元素，其中k个元素不为0
+X = zeros(n, 1);
+index = randperm(n, k);
+val = randn(1, k);
+X(index) = val;
+
+% 得到观测矩阵（压缩后）
+A = D * X;
+
+%%
+% % 通过cVMAP算法完成恢复X，得到恢复后信号
+lambda = ones(n, 1) ./ 10;
+[x_hat_wl, x_hat_d] = cVAMP(A, D, lambda, 1e-4, 200);
+
+%%
+% 显示结果
+figure;
+subplot(3, 1, 1)
+stem(X);
+title('origin signal')
+subplot(3, 1, 2)
+stem(x_hat_wl);
+title('restored signal')
+subplot(3, 1, 3)
+stem(X - x_hat_wl);
+title('differ')