Deterministic complex-valued measurement matrices based on Berlekamp-Justesen codes

Author

Lu Liu ; Xin-Ji Liu ; Shu-Tao Xia

Author_Institution

Grad. Sch. at Shenzhen, Tsinghua Univ., Shenzhen, China

fYear

2014

fDate

9-13 July 2014

Firstpage

723

Lastpage

727

Abstract

Nowadays deterministic construction of measurement matrices is a hot topic in compressed sensing. In this paper, we propose two classes of deterministic complex-valued measurement matrices based on Berlekamp-Justesen codes. Row and column numbers of these matrices are tunable through row and column puncturing. Moreover, the proposed matrices are obtained from circular matrices, thus the storage costs of them are relatively low and both the sampling and recovery process can be simpler. Simulation results show that the proposed matrices perform better than Gaussian random matrices and some other deterministic measurement matrices under OMP recovery, especially for image reconstruction.

Keywords

Gaussian processes; compressed sensing; matrix algebra; Berlekamp-Justesen codes; Gaussian random matrices; circular matrices; column puncturing; compressed sensing; deterministic complex valued measurement matrices; deterministic construction; image reconstruction; Chirp; Compressed sensing; Discrete Fourier transforms; Image reconstruction; Matrices; Parity check codes; Sparse matrices; Berlekamp-Justesen; LDPC; complex-valued matrices; compressed sensing; measurement matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Signal and Information Processing (ChinaSIP), 2014 IEEE China Summit & International Conference on

Conference_Location

Xi´an

Print_ISBN

978-1-4799-5401-8

Type

conf

DOI

10.1109/ChinaSIP.2014.6889339

Filename

6889339