Chaotic Binary Sensing Matrices

Abstract

As an emerging field for sampling paradigms, compressive sensing (CS) can sample and represent signals at a sub-Shannon–Nyquist rate. To realize CS from theory to practice, the random sensing matrices must be substituted by faster measurement operators that correspond to feasible hardware architectures. In recent years, binary matrices have attracted much research interest because of their multiplier-less and faster data acquisition. In this work, we aim to pinpoint the potential of chaotic binary sequences for constructing high-efficiency sensing implementations. In particular, the proposed chaotic binary sensing matrices are verified to meet near-optimal theoretical guarantees in terms of both the restricted isometry condition and coherence analysis. Simulation results illustrate that the proposed chaotic constructions have considerable sampling efficiency comparable to that of the random counterparts. Our framework encompasses many families of binary sensing architectures, including those formed from Logistic, Chebyshev, and Bernoulli binary chaotic sequences. With many chaotic binary sensing architectures, we can then more easily apply CS paradigm to various fields.