A Construction of Sparse Deterministic Measurement Matrices

Yubo LI  Hongqian XUAN  Dongyan JIA  Shengyi LIU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.11   pp.1575-1579
Publication Date: 2019/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1575
Type of Manuscript: LETTER
Category: Digital Signal Processing
Keyword: 
compressed sending (CS),  measurement matrix,  finite fields,  restricted isometry property (RIP),  

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Summary: 
In this letter, a construction of sparse measurement matrices is presented. Based on finite fields, a base matrix is obtained. Then a Hadamard matrix or a discrete Fourier transform (DFT) matrix is nested in the base matrix, which eventually formes a new deterministic measurement matrix. The coherence of the proposed matrices is low, which meets the Welch bound asymptotically. Thus these matrices could satisfy the restricted isometry property (RIP). Simulation results demonstrate that the proposed matrices give better performance than Gaussian counterparts.