Application of Coherence Function to the Analysis of Compressive Sensing

Abstract

Compressive sensing has been developed for the sampling of sparse or compressible signals. Strong theorems state that when a signal is sufficiently sparse, its samples can be accurately recovered from random sub-Nyquist measurements. As a consequence, compressive sensing is emerging as a part of various applications, such as image processing, biomedical problems or audio signal processing. Designing a compressive sensing application comprises the selection of many parameters, e.g. data acquisition scheme, compression ratio, reconstruction algorithm, etc. To make these decisions experimentally, a simple criterion to compare several options can prove to be helpful. This paper proposes to use the coherence function as a criterion to evaluate the quality of a signal transmission via compressive sensing. After a brief review of compressive sensing, the usage of the coherence function is presented. Simulation examples illustrate how it can help making the design decisions.