A performance comparison of measurement matrices in compressive sensing

Abstract

Summary Compressive sensing involves 3 main processes: signal sparse representation, linear encoding or measurement collection, and nonlinear decoding or sparse recovery. In the measurement process, a measurement matrix is used to sample only the components that best represent the signal. The choice of the measurement matrix has an important impact on the accuracy and the processing time of the sparse recovery process. Hence, the design of accurate measurement matrices is of vital importance in compressive sensing. Over the last decade, a number of measurement matrices have been proposed. Therefore, a detailed review of these measurement matrices and a comparison of their performances are strongly needed. This paper explains the foundation of compressive sensing and highlights the process of measurement by reviewing the existing measurement matrices. It provides a 3‐level classification and compares the performance of 8 measurement matrices belonging to 4 different types using 5 evaluation metrics: the recovery error, processing time, recovery time, covariance, and phase transition diagram. The theoretical performance comparison is validated with experimental results, and the results show that the Circulant, Toeplitz, and Hadamard matrices outperform the other measurement matrices.

A Bat-Inspired Sparse Recovery Algorithm for Compressed Sensing

“…Candes and Tao proved that the Gaussian random matrix [2, 21, 22] with independent identically distribution can be a universal measurement matrix. Therefore, the measurement matrices in these experiments are the Gaussian random matrix with the size of m × n .…”

Metrics for Evaluating the Efficiency of Compressing Sensing Techniques

“…In [9], the authors compared the efficiency of their recovery algorithm using the mean square error. In [10], the authors compared the performance of the sampling matrices using metrics, namely recovery error, processing time, recovery time, covariance, and phase transition diagram. In [11], the authors evaluated the compressive sensing technique based on the recovery success rate, reconstruction error, recovery time, compression ratio, and processing time.…”

Compressive spectrum sensing using chaotic matrices for cognitive radio networks

“…() Deterministic matrices have an advantage over random ones since they are easier to generate and store, which reduces the complexity of the system . It has also been shown that deterministic matrices speed up the reconstruction process . In any case, the sensing matrix must be known in order for the signal to be reconstructed.…”

“…11 It has also been shown that deterministic matrices speed up the reconstruction process. 10 In any case, the sensing matrix must be known in order for the signal to be reconstructed. This means that, in a collaborative network, the sensing matrix must either be fixed or be actively shared among the nodes of the network, which is the motivation for using chaotic matrices in this paper.…”