稀疏信号恢复问题解的个数  

Number of Solution for the Sparse Signal Recovery Problem

作　　者：廖安平[1] 杨苗[1] 谢家新 沈坤[2] 

机构地区：[1]湖南大学数学与计量经济学院,长沙410082 [2]湖南师范大学物理与信息科学学院,长沙410081

出　　处：《工程数学学报》2015年第5期643-649,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11271117);湖南省自然科学基金(2015JJ6070)~~

摘　　要：稀疏信号恢复是信号处理研究领域中的重要问题,本文研究基于线性测量的稀疏信号恢复问题解的个数.在无噪测量下,采用组合分析方法,给出了稀疏信号恢复问题解的个数的一个上界,并通过构造一个特殊的线性测量矩阵,证明了该上界是最佳的.此外,如果测量矩阵还满足一定的条件,则该上界可减小.所得结果为特定情形下求解稀疏信号恢复问题提供了一种有限搜索的新思路.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.

关 键 词：压缩感知 稀疏信号恢复 线性测量 

分 类 号：TN911.7[电子电信—通信与信息系统] O151.26[电子电信—信息与通信工程]