83 lines
1.8 KiB
Matlab
Executable File
83 lines
1.8 KiB
Matlab
Executable File
% Input: y,A,lambda,tau,Kit
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% Output: x_hat_wl,x_hat_d
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% Main structure of cVAMP
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function [x_hat_wl, x_hat_d] = cVAMPro(y, A, lambda, tau, Kit)
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% Initialization
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[M, N] = size(A);
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gamma = M / N;
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k = 0;
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p = ctranspose(A) * y;
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h_1 = p;
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Q_1 = gamma;
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tau_d = 1;
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% Iteration
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while ((k < Kit) && (tau_d > tau))
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% Factorized Part
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x_1 = ST(h_1, lambda, Q_1);
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chi_1 = F1(x_1, lambda, Q_1);
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% Message Passing
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h_2 = x_1 / chi_1 - h_1;
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Q_2 = 1 / chi_1 - Q_1;
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% Gaussian Part
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t1 = (p + h_2) / Q_2;
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t2 = ctranspose(A) * (A * (p + h_2)) / ((Q_2 + 1) * Q_2);
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x_2 = t1 - t2;
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chi_2 = gamma / (Q_2 + 1) + (1 - gamma) / Q_2;
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% Message Passing
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h_1_next = x_2 ./ chi_2 - h_2;
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Q_1_next = 1 / chi_2 - Q_2;
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tau_d = norm(h_1_next - h_1, Inf) / norm(h_1_next, Inf);
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k = k + 1;
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% output
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x_hat_wl = x_1;
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x_hat_d = h_1_next / Q_1_next;
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% next
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h_1 = h_1_next;
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Q_1 = Q_1_next;
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end
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end
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% SoftThreshold function
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function x = ST(h_1, lambda, Q_1)
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[N, M] = size(h_1);
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x = zeros(N, M);
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for i = 1:N
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sign = h_1(i) ./ abs(h_1(i));
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diff = abs(h_1(i)) - lambda(i);
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x(i) = sign .* (diff ./ Q_1) .* SF(diff);
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end
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end
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% Heaviside's step function
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function v = SF(a)
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if a > 0
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v = 1;
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elseif a == 0
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v = 0; % at zero points
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else
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v = 0;
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end
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end
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% Calculation of chi_1
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function chi_1 = F1(x_1, lambda, Q_1)
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[N, M] = size(x_1);
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count = 0;
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for i = 1:N
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temp = Q_1 * abs(x_1(i)) + lambda(i);
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count = count + (2 - lambda(i) / temp) * SF(abs(x_1(i)));
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% count = count + (2-lambda(i)/temp) * (abs(x_1(i)) > 1e-4);
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end
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chi_1 = count / (2 * N * Q_1);
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end
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