Compressive sensing using chaotic sequence based on Chebyshev map

Abstract

Compressive sensing is a new sampling theory which allows for signal sampling at a sub-Nyquist rate. In order to ensure exact reconstruction from very few measurements, one should design a stable sensing matrix, which satisfies restricted isometry property (RIP), such that it preserves the significant information of original signal in sensing procedure. In this paper, a novel sensing matrix is proposed based on the Chebyshev chaotic system, and the Chebyshev chaotic sensing matrix (CsCSM) is proved to satisfy RIP with overwhelming probability. Numerical simulations show that the CsCSM is sufficient to guarantee exact recovery, which is similar to random sensing matrices such as Gaussian sensing matrix. However, the CsCSM can be easily implemented in hardware circuit and will be more beneficial in some applications which require security and privacy, as opposed to random sensing matrices.