  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.
