Restricted Structural Random Matrix for Compressive Sensing
This addresses the problem of balancing efficiency and security in compressive sensing for applications like signal processing, though it appears incremental as it builds on existing matrix designs.
The paper tackled the tradeoff in compressive sensing between improving sensing/compressing efficiency and maintaining security by introducing a novel sampling matrix called Restricted Structural Random Matrix (RSRM), which unifies frame-based and block-based sensing with global smoothness prior and shows comparable reconstruction performance to state-of-the-art methods.
Compressive sensing (CS) is well-known for its unique functionalities of sensing, compressing, and security (i.e. CS measurements are equally important). However, there is a tradeoff. Improving sensing and compressing efficiency with prior signal information tends to favor particular measurements, thus decrease the security. This work aimed to improve the sensing and compressing efficiency without compromise the 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 (equally important) of multiple randomly sub-sampled signals, which was restricted to be the low-resolution signals (equal in energy), thereby, its observations are equally important. RSRM was proven to satisfies the Restricted Isometry Property and shows comparable reconstruction performance with recent state-of-the-art compressive sensing and deep learning-based methods.