Dealing with large matrices in compressive sensing

Following code demonstrates compressive sensing. The length of the input signal x used is N =1024 samples. The size of the DFT matrix B would be N^2. But once the signal length is large, say 214688, the DFT matrix (B = dftmtx (N)) becomes too large and the system runs out of memory. Is there a efficient way to generate this matrix and manipulate it? I need this matrix to generate the measurement matrix A by randomly selecting K number of rows from B and also to take time measurements y = (A * fft(x)).

%Author: Osama Ullah Khan,
%        Phd Student, University of Michigan-Ann Arbor.
%        Email: [e-mail]
%        Version: 1.0
%
%This code demonstrate compressive sensing example. In this
%example the signal is sparse in frequency domain and random samples
%are taken in time domain.

close all;
clear all;

%length of the signal
N=1024;

%Number of random observations to take
K=256;

%Discrete frequency of two sinusoids in the input signal
k1=29;
k2=100;

n=0:N-1;

%Sparse signal in frequency domain.
x=sin(2*pi*(k1/N)*n)+sin(2*pi*(k2/N)*n);

figure;
subplot(2,1,1);
plot(x)
grid on;
xlabel('Samples');
ylabel('Amplitude');
title('Original Signal,1024 samples with two different frequency sinsuoids');

xf=fft(x);

subplot(2,1,2);
plot(abs(xf))
grid on;
xlabel('Samples');
ylabel('Amplitude');
title('Frequency domain, 1024 coefficients with 4-non zero coefficients');

%creating dft matrix
B=dftmtx(N);
Binv=inv(B);

%Selecting random rows of the DFT matrix
q=randperm(N);

%creating measurement matrix
A=Binv(q(1:K),:);

%taking random time measurements
y=(A*xf);

% %Calculating Initial guess
% x0=A'*y;
% 
% %Running the recovery Algorithm
% tic
% xp=l1eq_pd(x0,A,[],y,1e-5);
% toc

% cvx_begin
%     variable xp(N)
%     minimize( norm( xp, 1 ) )
%     subject to
%        y == A * xp;         
% cvx_end

% [xp,r,g,info] = spg_bp(A,y );
% 
% %recovered signal in time domain
% xprec=real(Binv*xp);
% 
% figure;
% subplot(2,1,1)
% plot(abs(xf))
% grid on;
% xlabel('Samples');
% ylabel('Amplitude');
% title('Original Signal, Discrete Fourier Transform');
% 
% subplot(2,1,2)
% plot(abs(xp),'r')
% grid on;
% xlabel('Samples');
% ylabel('Amplitude');
% title(sprintf('Recovered Signal, Discrete Fourier Transform sampled with %d samples',K));
% 
% figure;
% subplot(2,1,1);
% plot(x)
% grid on;
% xlabel('Samples');
% ylabel('Amplitude');
% title('Original Signal,1024 samples with two different frequency sinsuoids');
% 
% subplot(2,1,2)
% plot(xprec,'r')
% grid on;
% xlabel('Samples');
% ylabel('Amplitude');
% title(sprintf('Recovered Signal in Time Domain'));
%

Answer 1

[ahmed nebli]

u need to store your matrices in a .mat file, then call that .mat file using function called matfile, this function access and change variables directly in MAT-files, without loading into memory.

this would make you not loose the memory. for further informations see this link: https://www.mathworks.com/help/matlab/ref/matfile.html