Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Number of Solution for the Sparse Signal Recovery Problem

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  • 1- College of Mathematics and Econometrics, Hunan University, Changsha 410082
    2- College of Physics and Information Science, Hunan Normal University, Changsha 410081

Received date: 2014-07-01

  Accepted date: 2014-12-27

  Online published: 2014-12-27

Supported by

The National Natural Science Foundation of China (11271117); the Natural Science Foundation of Hunan Province (2015JJ6070).

Abstract

This paper is concerned with the number of solution to sparse signal recovery problem based on linear measurements, which is an important problem in signal processing. In the noiseless measurement case, by taking advantage of the combinatorial analysis method, an upper bound is established for the number of solution to the sparse signal recovery problem, and by constructing a special linear measuring matrix, the best of the upper bound is proved as well. Moreover, if the measuring matrix satisfies some conditions, the upper bound could be improved. Based on these results, some new ideas of a finite search can be employed to solve the sparse signal recovery problem in some special cases.

Cite this article

LIAO An-ping, YANG Miao, XIE Jia-xin, SHEN Kun . Number of Solution for the Sparse Signal Recovery Problem[J]. Chinese Journal of Engineering Mathematics, 2015 , 32(5) : 643 -649 . DOI: 10.3969/j.issn.1005-3085.2015.05.002

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