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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.E102A
No.11
pp.15751579 Publication Date: 2019/11/01
Online ISSN: 17451337
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),
Full Text: PDF(200.8KB)>>
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.

