Candes.m
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Revision as of 17:19, 1 July 2008
%Emmanuel Candes, California Institute of Technology, June 6, 2007
%IMA Summerschool
n = 512; % Size of the signal
m = 64; % Number of samples (undersample by a factor 8)
k = 0:n-1; t = 0:n-1;
F = exp(-i*2*pi*k'*t/n)/sqrt(n); % Fourier matrix
freq = randsample(n,m);
A = [real(F(freq,:));
imag(F(freq,:))]; % Incomplete Fourier matrix
S = 28;
support = randsample(n,S);
x0 = zeros(n,1); x0(support) = randn(S,1);
b = A*x0;
%% Solve 11 using CVX (Boyd)
cvx_begin
variable x(n);
minimize(norm(x,1));
A*x == b;
cvx_end
norm(x - x0)/norm(x0)
figure, plot(1:n,x0,'b*',1:n,x,'ro'), legend('original','decoded')