An Improved Toeplitz Measurement Matrix for Compressive Sensing

Abstract

Compressive sensing (CS) takes advantage of the signal's sparseness in some domain, allowing the entire signal to be efficiently acquired and reconstructed from relatively few measurements. A proper measurement matrix for compressive sensing is significance in above processions. In most compressive sensing frameworks, random measurement matrix is employed. However, the random measurement matrix is hard to implement by hardware. So the randomness of the measurement matrix leads to the poor performance of signal reconstruction. In this paper, Toeplitz matrix is employed and optimized as a deterministic measurement matrix. A hardware platform for signal efficient acquisition and reconstruction is built by field programmable gate arrays (FPGA). Experimental results demonstrate the proposed approach, compare with the existing state-of-the-art method, and have the highest technical feasibility, lowest computational complexity, and least amount of time consumption in the same reconstruction quality.