Combinatorial Optimization Based on Conjugate Gradient and Orthogonal Triangular Decomposition for Sparse Recovery

摘要

Sparse recovery is a challenging theme in signal processing and image processing. The basic goal is to reconstruction of sparse images or signals from very few samples by means of solving a tractable optimization problem. An important aspect of sparse recovery is to develop the recovery performance in the presence of noise. In this article, we propose the matching pursuit algorithm of combinatorial optimization based Conjugate Gradient Lest Squares (CGLS) and Lest Squares QR (LSQR). We use non-negative matrix factorization for measuring discrepancy of solution sequence between CGLS and LSQR, and represent combinatorial optimization based CGLS and LSQR to choose optimal solution sequences. The experiments indicate our method is extended to the case where target signal has been corrupted by noise, it demonstrates perfectly recovery ability of signal with noise.