40 lines
1.2 KiB
Matlab
Executable File
40 lines
1.2 KiB
Matlab
Executable File
function [x_hat, sigma_w_2, threshold] = debiased_LASSO(A, y_noise, P_fa, noise_sigma_2, LASSO_lambda)
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if nargin < 5
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LASSO_lambda = 1e-1;
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end
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sz = size(A);
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N = sz(2);
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gamma = sz(1) / sz(2);
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cvx_begin quiet
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variable x_LASSO(N) complex
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minimize(LASSO_lambda * norm(x_LASSO, 1) + norm(y_noise - A * x_LASSO, 2))
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cvx_end
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rho_active = sum(abs(x_LASSO) > 1e-3) / N;
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Q_hat = (gamma - rho_active) / (1 - rho_active);
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Rho = sum((abs(x_LASSO) > 1e-3) .* (2 - LASSO_lambda ./ (Q_hat * abs(x_LASSO) + LASSO_lambda))) / 2 / N;
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diff = 1;
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while (diff > 1e-4)
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Rho_pre = Rho;
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Rho = sum((abs(x_LASSO) > 1e-3) .* (2 - LASSO_lambda ./ ((gamma - Rho) / (1 - Rho) * abs(x_LASSO) + LASSO_lambda))) / 2 / N;
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diff = abs(Rho - Rho_pre);
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end
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Q_hat = (gamma - Rho) / (1 - Rho);
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x_d_CROD = x_LASSO + A' * (y_noise - A * x_LASSO) / Q_hat;
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x_hat = x_d_CROD;
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RSS = 1 / sz(1) * norm(y_noise - A * x_LASSO, 2) ^ 2;
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sigma_w_2 = (gamma * (1 - gamma)) / ((gamma - Rho) ^ 2) * RSS + noise_sigma_2;
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threshold = -sigma_w_2 * log(P_fa);
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xx = x_LASSO;
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FAR_M = 1 / gamma;
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xx(FAR_M+1: 2*FAR_M) = xx(FAR_M+1: 2*FAR_M) - 1;
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xx = real(xx);
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end
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