function [x_hat, threshold] = debiased_LASSO(A, y_noise, P_fa, noise_sigma_2)
    sz = size(A);
    N = sz(2);
    LASSO_lambda = 2;

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

    cvx_begin quiet
        variable x_LASSO(N) complex
        minimize(LASSO_lambda * norm(x_LASSO, 1) + norm(y_noise - A * x_LASSO, 2))
    cvx_end

    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(2) * 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);
    
end