A large class of chaotic sensing matrices for compressed sensing

Abstract

Compressed sensing is a revolutionary sampling framework at a sub-Nyquist rate, which relies potentially on sensing matrix. In this paper, a large class of chaotic sensing matrices with low complexity, hardware-friendly implementation and desirable sampling efficiency is proposed based on topologically conjugate chaotic systems (TCcSs). Specifically, we first elaborate an independently and identically distributed chaotic stream, which is generated from a TCcS via our customized zone matching algorithm. Then, the chaotic stream is employed to construct the novel chaotic sensing matrix. Our framework encompasses various families of TCcSs for establishing sensing matrices, such as TCcSs of Tent chaotic system. Moreover, the mutual coherence of the proposed sensing matrices is investigated, and it shows that this kind of chaotic sensing matrices has similar sampling efficiency to that of the state-of-the-art sensing matrices. Experimental performances verify the correctness of the theoretical analysis and illustrate that the proposed matrices can provide comparable results against the existing ones.