Random measurement matrix needs large storage space

huge memory requirements for reconstruction

and high computational cost

which are not suitable for large-scale applications. To reduce the storage space of random measurement matrix for compressed sensing (CS)

a new sampling approach for CS with semi-tensor product (STP-CS) is proposed. The STP-CS approach generates a random matrix

where the row and column numbers of the matrix are smaller than that for conventional CS. Then we optimize the matrix by the singular value decomposition (SVD) approach

after sampling with the matrix

we estimate the solutions of the sparse vector with the smooth

l

0

-norm minimization alg

orithm. Numerical experiments were conducted using gray-scale images

the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM) of the reconstruction images were compared with the random matrices with different dimensions. Comparisons were also conducted with other random measurement matrix and other low storage techniques. Numerical experiment results show that the STP-CS can effectively reduce the storage space of the random measurement matrix to 1/256 of that for conventional CS

while maintaining the reconstruction performance.