Chaotic Compressive Sampling Matrix: Where Sensing Architecture Meets Sinusoidal Iterator

A key issue in compressive sampling is to construct a sensing matrix that is stable and easy to design in hardware. In this paper, a novel chaotic sensing matrix is proposed by establishing a connection between sensing architecture and chaotic sinusoidal iterator. Based on a chaining method with the volumetric argument, we show that the proposed sinusoidal chaotic sensing matrix yields the well-known restricted isometry property. Numerical experiments with time-sparse signals and natural images are reported to compare the sampling performance between chaotic sensing constructions and random ones. The obtained results indicate that the proposed chaotic matrix is always able to exhibit similar or superior performance with respect to its counterparts. Moreover, the proposed construction can be easily implemented on the field-programmable gate array environment. Our framework may guide other researchers to extend the proposed method for other chaotic systems as well.