Optimized structured sparse sensing matrices for compressive sensing

• DOI: 10.1016/j.sigpro.2019.02.004
• Publication Date: 2019-02-05T02:07:53Z
• Authors: Tao Hong; Xiao Li; Zhihui Zhu; Qiuwei Li
• Keywords: Signal Processing (eess.SP); FOS: Computer and information sciences; Computer Science - Machine Learning; FOS: Electrical engineering, electronic engineering, information engineering; Electrical Engineering and Systems Science - Signal Processing; Machine Learning (cs.LG)

We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing matrix through minimizing the distance between the Gram matrix of the equivalent dictionary and the target Gram of matrix holding small mutual coherence. Moreover, a regularization is added to enforce the robustness of the optimized structured sparse sensing matrix to the sparse representation error (SRE) of signals of interests. An alternating minimization algorithm with global sequence convergence is proposed for solving the corresponding optimization problem. Numerical experiments on synthetic data and natural images show that the obtained structured sensing matrix results in a higher signal reconstruction than a random dense sensing matrix.<br/>2 tables, 10 figures<br/>