cs_exam.m

压缩传感理论仿真的一个实际例子

clear
n=512;       %size of the signal
m=64;        %Number of samples(under sample by a factor)
 
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;
 
 
cvx_begin
   variable  x(n);
   minimize(norm(x,1));
   subject to
   A*x==b;
cvx_end
 
norm(x-x0)/norm(x0);
figure;
plot(1:n,x0,'b*',1:n,x,'ro'), legend('original','decoded');