function [x_hat, sigma_w_2, threshold] = debiased_LASSO_FISTA(A, y_noise, P_fa, noise_sigma_2, LASSO_lambda)

    if nargin < 5
        LASSO_lambda = 1e-1;
    end
    
    sz = size(A);
    N = sz(2);

    gamma = sz(1) / sz(2);

    x_LASSO = FISTA(y_noise, A, LASSO_lambda, 1e-5);
    
    rho_active = sum(abs(x_LASSO) > 1e-3) / N;
    Q_hat = (gamma - rho_active) / (1 - rho_active);
    Rho = sum((abs(x_LASSO) > 1e-3) .* (2 - LASSO_lambda ./ (Q_hat * abs(x_LASSO) + LASSO_lambda))) / 2 / N;
    diff = 1;

    while (diff > 1e-4)
        Rho_pre = Rho;
        Rho = sum((abs(x_LASSO) > 1e-3) .* (2 - LASSO_lambda ./ ((gamma - Rho) / (1 - Rho) * abs(x_LASSO) + LASSO_lambda))) / 2 / N;
        diff = abs(Rho - Rho_pre);
    end

    Q_hat = (gamma - Rho) / (1 - Rho);
    x_d_CROD = x_LASSO + A' * (y_noise - A * x_LASSO) / Q_hat;
    x_hat = x_d_CROD;

    RSS = 1 / sz(1) * norm(y_noise - A * x_LASSO, 2) ^ 2;
    sigma_w_2 = (gamma * (1 - gamma)) / ((gamma - Rho) ^ 2) * RSS + noise_sigma_2;
    threshold = -sigma_w_2 * log(P_fa);
    xx = x_LASSO;
    FAR_M = 1 / gamma;
    mean_xx = mean(xx(FAR_M+1: 2*FAR_M));
end