An Optimization Method for Measurement Matrix Based on Double Decomposition

Abstract

This paper introduces a novel method of measurement matrix in compressed sensing. In order to overcome the difficulties associated with coherence of measurement matrix, we propose double optimization methods by eigenvalue decomposition and singular value decomposition under mild conditions. An efficient algorithm (SVD-EIG) is used to recover sparse inputs from the optimized measurement matrix, based on the adaptation of the optimized matrix by eigenvalue decomposition. Lastly, compared with the other methods as the same sampling rate, we demonstrate through simulations that SVD-EIG algorithm can improve accuracy and probability of the reconstruction.