Separable Compressive Imaging Method Based on Singular Value Decomposition

When facing the compressive imaging problem that the measurement matrix has too large dimension, separable compressive sensing (SCS) can effectively achieve this problem at a cost of a certain percentage of additional measurements. However, the both separable measurement matrices in existing separable compressive sensing method should be row-normalized orthogonal random matrix, which limits its application significantly. In this paper, the method of singular value decomposition (SVD) is introduced into separable compressive sensing measurement process, which can effectively achieve the separation of measurement matrix and reconstruction matrix: the design of the measurement matrix in sensing stage is more to consider the physical properties for easy implementations, such as the deterministic structure of Toeplitz or Circulant matrices and etc; in the reconstruction stage, it is more to consider the optimization of reconstruction matrix. Through the introduction of singular value decomposition method to optimize the measurement matrix in reconstruction stage, the reconstruction performance can be effectively facilitated, especially for Toeplitz and Circulant matrix in large-scale image compressive reconstruction. Numerical results demonstrate the validity of our proposed method.