Restricted Structural Random Matrix for compressive sensing

Abstract Compressive sensing (CS) is well-known for its unique functionalities of sensing, compressing, and security (i.e. equal importance of CS measurements). However, there is a tradeoff. Improving sensing and compressing efficiency with prior signal information tends to favor particular measurements, thus decreasing security. This work aimed to improve the sensing and compressing efficiency without compromising security with a novel sampling matrix, named Restricted Structural Random Matrix (RSRM). RSRM unified the advantages of frame-based and block-based sensing together with the global smoothness prior (i.e. low-resolution signals are highly correlated). RSRM acquired compressive measurements with random projection of multiple randomly sub-sampled signals, which was restricted to low-resolution signals (equal in energy), thereby its observations are equally important. RSRM was proven to satisfy the Restricted Isometry Property and showed comparable reconstruction performance with recent state-of-the-art compressive sensing and deep learning-based methods.