Candes.m

From Wikimization

Revision as of 17:19, 1 July 2008 by Dattorro (Talk | contribs)
(diff) ←Older revision | Current revision (diff) | Newer revision→ (diff)
Jump to: navigation, search
%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')
Retrieved from "http://www.convexoptimization.com/wikimization/index.php/Candes.m"
Personal tools