压缩感知（十）

压缩感知仿真验证

一维信号重建实验

clear; 
close all;
 
choice_transform=1;       
choice_Phi=0;             
n = 512;
t = [0: n-1];
f = cos(2*pi/256*t)   sin(2*pi/128*t);   % 
n = length(f);
a = 0.2;                    
m = double(int32(a*n));

switch choice_transform
    case 1
        ft = dct(f);
        disp(‘ft = dct(f)‘)
    case 0
        ft = fft(f);
        disp(‘ft = fft(f)‘)
end
 
disp([‘ÐÅºÅÏ¡Êè¶È£º‘,num2str(length(find((abs(ft))>0.1)))])
figure(‘name‘, ‘A Tone Time and Frequency Plot‘);
subplot(2, 1, 1);
plot(f);
xlabel(‘Time (s)‘); 
% ylabel(‘f(t)‘);
subplot(2, 1, 2);
 
switch choice_transform
    case 1
        plot(ft)
        disp(‘plot(ft)‘)
    case 0
        plot(abs(ft));
        disp(‘plot(abs(ft))‘)
end
xlabel(‘Frequency (Hz)‘); 
% ylabel(‘DCT(f(t))‘);

switch choice_Phi
    case 1
        Phi = PartHadamardMtx(m,n);       
    case 0
        Phi = sqrt(1/m) * randn(m,n);    
end
f2 = (Phi * f‘)‘;       
% f2 = f(1:2:n);
 
switch choice_transform
    case 1
        Psi = dct(eye(n,n));           
        disp(‘Psi = dct(eye(n,n));‘)
    case 0
        Psi = inv(fft(eye(n,n)));      
        disp(‘Psi = inv(fft(eye(n,n)));‘)
end
 
A = Phi * Psi;                    % A = Phi * Psi
cvx_begin;
    variable x(n) complex;
%     variable x(n) ;
    minimize(norm(x,1));
    subject to
      A*x == f2‘;
cvx_end;
 
figure;
subplot(2,1,2);
switch choice_transform
    case 1
        plot(real(x));
        disp(‘plot(real(x))‘)
    case 0
        plot(abs(x));
        disp(‘plot(abs(x))‘)
end
 
title(‘Using L1 Norm£¨Frequency Domain£©‘);
 
%  ylabel(‘DCT(f(t))‘); xlabel(‘Frequency (Hz)‘);
switch choice_transform
    case 1
        sig = dct(real(x));
        disp(‘sig = dct(real(x))‘)
    case 0
        sig = real(ifft(full(x)));
        disp(‘sig = real(ifft(full(x)))‘)
end
subplot(2,1,1);
plot(f)
hold on;plot(sig);hold off
title(‘Using L1 Norm (Time Domain)‘);
% ylabel(‘f(t)‘); xlabel(‘Time (s)‘);
legend(‘Original‘,‘Recovery‘)

for K = 1:100
    theta = CS_OMP(f2,A,K);
    %     figure;plot(dct(theta));title([‘K=‘,num2str(K)])
    switch choice_transform
        case 1
            re(K) = norm(f‘-(dct(theta)));
        case 0
            re(K) = norm(f‘-real(ifft(full(theta))));
    end
end
theta = CS_OMP(f2,A,find(re==min(min(re))));
disp([‘×î¼ÑÏ¡Êè¶ÈK=‘,num2str(find(re==min(min(re))))]);
% theta = CS_OMP(f2,A,10);
figure;subplot(2,1,2);
switch choice_transform
    case 1
        plot(theta);
        disp(‘plot(theta)‘)
    case 0
        plot(abs(theta));
        disp(‘plot(abs(theta))‘)
end
 
title([‘Using OMP(Frequence Domain)  K=‘,num2str(find(re==min(min(re))))])
 
switch choice_transform
    case 1
        sig2 = dct(theta);
        disp(‘sig2 = dct(theta)‘)
    case 0
        sig2 = real(ifft(full(theta)));
        disp(‘sig2 = real(ifft(full(theta)))‘)
end
 
subplot(2,1,1);plot(f);hold on;
plot(sig2)
hold off;
title([‘Using OMP(Time Domain)  K=‘,num2str(find(re==min(min(re))))]);
legend(‘Original‘,‘Recovery‘)