Fast and Efficient Compressive Sensing Using Structurally Random Matrices

TLDR

SRM is highly relevant for large‑scale, real‑time compressive sensing applications because it offers fast computation and supports block‑based processing. The paper introduces a new framework of fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). The framework pre‑randomizes a sensing signal by scrambling or sign‑flipping its samples, applies a fast transform, and then subsamples the transform coefficients to obtain the final sensing measurements. Theoretical analysis shows that SRM achieves sensing performance comparable to fully random matrices, and simulations confirm this and demonstrate its promising potential.

Abstract

This paper introduces a new framework of fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we pre-randomize a sensing signal by scrambling its samples or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the transform coefficients as the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical sensing performance comparable with that of completely random sensing matrices. Numerical simulation results verify the validity of the theory as well as illustrate the promising potentials of the proposed sensing framework.