Research on Measurement Matrix Based on Compressed Sensing Theory

Abstract

The basic theories of compressed sensing and measurement matrix are reviewed firstly, and then the equivalent conditions of the Null Space Property and Restricted Isometry Property for measurement matrix, the incoherence is introduced, including the theory and mathematical proof. On this basis, the construction methods and properties of several commonly used measurement matrices (random Gaussian matrix, Bernoulli random matrix, and Toeplitz matrix) are introduced. The time-domain sparse signals are used for simulation analysis. Simulation results show that the sparse signals can reconstructed when the measurement dimension M satisfies certain conditions. Considering the hardware implementation and storage space for matrix, and with the idea of circular matrix, this paper proposes a pseudo-random Bernoulli matrix. The simulation results show that the proposed matrix can realize reconstruction of sparse signal and is hardware-friendly, moreover, the required storage space is small.