Example of Compressive Sensing using Matlab

% l1eq example using linprog
% (l1 minimization with equality constraints).

%%%%%%%%%%%%%%%%%%%%%%%%
% Problem definition
% minimise    t(1) + ... + t(n)
% subject to  A*x = b
%             -x - t <= 0
%              x - t <= 0
%%%%%%%%%%%%%%%%%%%%%%%%

clear all
close all

% creating a signal

% signal length
N = 512;
% number of spikes in the signal
T = 20;
% number of observations to make
K = 120;

% random +/- 1 signal
x = zeros(N,1);
q = randperm(N);
x(q(1:T)) = sign(randn(T,1));

% measurement matrix
disp('Creating measurment matrix...');
A = randn(K,N);
A = orth(A')';
disp('Done.');
   
% observations
y = A*x;

% initial guess = min energy
x0 = A'*y;

% solve the LP
tic
[m, n] = size(A);
f = [zeros(n, 1); ones(n, 1)];
Ai = [-eye(n), -eye(n); eye(n), -eye(n)];
bi = zeros(2*n, 1);
Aeq = [A, zeros(m, n)];
beq = y;
xp = linprog(f, Ai, bi, Aeq, beq);
xp = xp(1:n);

toc

% Quality of reconstruction, difference between x an xp using l2

norma_l2_x = norm(xp-x)

% signal-to-distortion ratio (SDR)
ratio = norm(x)/norm(x - xp)

figure;
subplot(2,1,1);
plot(x);
xlabel('sinal original');
subplot(2,1,2);
plot(xp);
xlabel('Reconstrucao usando linprog');



--

Juan Gabriel Colonna

CV: http://lattes.cnpq.br/9535853909210803