Compressive sampling with chaotic dynamical systems

TL;DR

This paper explores the use of chaotic dynamical systems to generate measurement matrices for compressive sampling, comparing their effectiveness to traditional random matrices and analyzing the impact of correlation.

Contribution

It introduces the use of Chua, Lorenz, and Rossler systems for measurement matrix construction and evaluates their performance in signal recovery.

Findings

Chua and Lorenz sequences are suitable for measurement matrices.

Chaotic sequences perform comparably to Gaussian and Bernoulli matrices.

Correlation has minimal impact on reconstruction probability.

Abstract

We investigate the possibility of using different chaotic sequences to construct measurement matrices in compressive sampling. In particular, we consider sequences generated by Chua, Lorenz and Rossler dynamical systems and investigate the accuracy of reconstruction when using each of them to construct measurement matrices. Chua and Lorenz sequences appear to be suitable to construct measurement matrices. We compare the recovery rate of the original sequence with that obtained by using Gaussian, Bernoulli and uniformly distributed random measurement matrices. We also investigate the impact of correlation on the recovery rate. It appears that correlation does not influence the probability of exact reconstruction significantly.