Research on Construction of Measurement Matrix Based on Welch Bound

Abstract

Compressive sensing (CS) is a new theory of data acquisition and reconstruction. It permits the data of interest being sampled at a sub-Nyquist rate, meanwhile still allowing perfect reconstruction of data from highly incomplete measurements. During this process, the construction of measurement matrix is undoubtedly the key point. However, the traditional random measurement matrices, though having good performance, are difficult to implement in hardware and lack the ability of dealing with large signals. In this paper, we construct a series of novel measurement matrices (HWKM and HWCM) based on Welch bound, by sifting the basis matrix based on Hadamard matrix. Therefore, the proposed matrices are deterministic measurement, which can be easily designed in hardware. Specially, it is proved to have low coherence, which can even approach to Welch bound. Experimental results show that the proposed matrices, compared with traditional measurement matrices, not only have considerable reconstruction performance in terms of reconstruction error and the signal-to-noise ratio, but also accelerate recovery time.