State of the Art and Prospects of Structured Sensing Matrices in Compressed Sensing

TL;DR

This paper reviews structured sensing matrices in compressed sensing, highlighting their advantages in simplifying hardware, reducing computational costs, and maintaining high recovery performance compared to random matrices.

Contribution

It provides a comprehensive review of structured sensing matrices based on restricted isometry property and coherence, comparing their measurement efficiency and universality.

Findings

Structured matrices have advantages like simple construction and fast calculation.

Compared measurement numbers and universality across different structured matrices.

Structured matrices enable practical hardware implementation in compressed sensing.

Abstract

Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction. Many structured sensing matrices have been proposed recently to simplify the sensing scheme and the hardware implementation in practice. Based on the restricted isometry property and coherence, couples of existing structured sensing matrices are reviewed in this paper, which have special structures, high recovery performance, and many advantages such as the simple construction, fast calculation and easy hardware implementation. The number of measurements and the universality of different structure matrices are compared.