147 lines
3.4 KiB
Matlab
147 lines
3.4 KiB
Matlab
% echo_mtx: echo data
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% A: chirp matrix
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% sigma_n: input noise standard deviation
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% lambda: LASSO weight
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% delta: convergence normalized difference
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% echo_r_mtx: range processing echo data
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% signal_n_o: output noise standard deviation
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function [ echo_r_mtx, sigma_n_o ] = range_process_CS(echo_mtx, A, sigma_n, lambda, delta)
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% parameters
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if nargin < 5
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delta = 2e-7;
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end
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[M, N] = size(A);
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[lenA, M, lenP] = size(echo_mtx);
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% normalization
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J1 = A*A';
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lambda_J=eig(J1);
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A = A / sqrt(lambda_J(end));
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echo_mtx = echo_mtx ./ sqrt(lambda_J(end));
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sigma_n = sigma_n / sqrt(lambda_J(end));
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% compressed sensing
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echo_r_mtx = zeros(lenA, N, lenP);
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for numA = 1: lenA
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for numP = 1: lenP
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sr = echo_mtx(numA, :, numP);
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y = transpose(sr);
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% LASSO
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x_FISTA = FISTA(y, A, lambda, delta);
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% debiased LASSO
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[x_d, sigma_w] = cal_debiased_LASSO(x_FISTA, A, y, lambda, sigma_n);
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echo_r_mtx(numA, :, numP) = x_d;
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end
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end
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% calculate output noise
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sigma_n_o = sigma_w;
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end
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% algorithm for LASSO
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% y: measurements
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% A: measurement matrix
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% lambda: LASSO weight
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% delta: convergence normalized difference
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% z: LASSO estimator
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function [z] = FISTA(y, A, lambda, delta)
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x_pre = A'*y;
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t = 1;
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z = x_pre;
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z_pre = z;
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t_pre = t;
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N = size(A, 2);
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diff = 1;
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E = eig(A'*A);
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L = E(end);
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temp1 = A'*y/L;
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temp2 = eye(N) - A'*A/L;
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k = 0;
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while((diff > delta) && (k < 1000))
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temp = temp1 + temp2 * z_pre;
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x = sft_thd(temp, lambda/L);
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t = 0.5*(1 + sqrt(1+4*t_pre*t_pre));
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z = x + (x - x_pre) * (t_pre-1) / t;
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diff = mean(abs(z_pre - z));
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x_pre = x;
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z_pre = z;
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t_pre = t;
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k = k + 1;
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end
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end
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% soft threshold function
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% x: processing object
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% thd: threshold
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% y: result
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function y = sft_thd(x, thd)
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if isequal(size(x), size(thd))
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tmp = abs(x);
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y = x;
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y(tmp <= thd) = 0;
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y(tmp > thd) = (tmp(tmp > thd) - thd(tmp > thd)) .* x(tmp > thd) ./ tmp(tmp > thd);
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else
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tmp = abs(x);
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y = x;
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y(tmp <= thd) = 0;
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y(tmp > thd) = (tmp(tmp > thd) - thd) .* x(tmp > thd) ./ tmp(tmp > thd);
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end
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end
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% calculate debiased LASSO estimator
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% x: LASSO estimator
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% A: measurement matrix
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% y: measurements
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% lambda: LASSO weight
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% sigma_n: input noise standard deviation
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% x_d: debiased LASSO estimator
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% sigma_d: equivalent noise standard deviation
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function [x_d, sigma_d] = cal_debiased_LASSO(x, A, y, lambda, sigma)
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[M, N] = size(A);
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gamma = M/N;
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hat_Q1 = gamma;
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[~, D] = eig(A'*A);
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d = diag(D);
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diff = 1;
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T = 1000;
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t = 0;
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while (t < T) && (diff > 1e-6)
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Q1_pre = hat_Q1;
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rho = mean((2 - lambda./(hat_Q1*abs(x) + lambda)).*(abs(x) > 1e-4))/2;
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hat_Q1 = rho/mean(1./(d + (1-rho)*hat_Q1/rho));
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diff = abs(Q1_pre - hat_Q1);
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t = t+1;
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end
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x_d = x + 1/hat_Q1*A'*(y - A*x);
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chi = rho/hat_Q1;
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hat_Q2 = 1/chi - hat_Q1;
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t = -hat_Q2;
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t_prime = -1/mean((1./(d+hat_Q2)).^2);
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G_prime = t + 1/chi;
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G_wprime = t_prime + 1/chi/chi;
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RSS = sum(abs(y - A*x).^2)/M;
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hat_chi = gamma*G_wprime/(2*G_prime-2*chi*G_wprime)*RSS +...
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(-G_wprime*gamma+G_prime*G_prime)/(2*G_prime-2*chi*G_wprime)*sigma^2;
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sigma_d = sqrt(2*hat_chi)/hat_Q1;
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end
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