一类稀疏约束下不适定反问题的求解  

An Kind of Ill-Posed Inverse Problem Solving with Sparsity Constraint

作　　者：赵玉娟[1,2] 郑宝玉[1] 陈守宁[1] 

机构地区：[1]南京邮电大学信号处理与传输研究院,江苏南京210003 [2]江苏第二师范学院数学与信息技术学院,江苏南京210013

出　　处：《数学的实践与认识》2015年第6期186-196,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61271240);江苏省自然科学基金重点项目资助(BK2010077);江苏省基础研究计划(自然科学基金)(BK2011756);江苏省高校自然科学研究资助项(11KJB510018);南京邮电大学科研基金项目(NY211009);江苏第二师范学院"十二五"科研规划第二期课题(Jsie2012yb03)

摘　　要：矩阵填充是一类稀疏先验下的不适定的反问题.首先阐述了矩阵填充的基本原理,指出只有当待求的矩阵满足不相关特性或秩-受限等距特性时,才有可能精确重构未知矩阵.Jain P等将矩阵的不相关特性与秩-受限等距特性联系起来,提出了仿射-受限等距特性,但没有说明秩-受限等距常数与不相关常数的关系,定理3给出了两者之间的的数值关系,有效的促进了矩阵填充的研究.接下来分析了矩阵填充中常用的几种算法,并在随后的仿真实验中对这几种算法的重构性能做了详细比较.Matrix completion is a kind of ill- posed inverse problem under sparsity constraint.This paper firstly explains the basis idea of matrix completion,and point out that only when the unknown matrix meets incoherent property or r- restricted isometry property,then we can possibly reconstruct this unknown matrix.P.Jain links incoherent property to r- restricted isometry property,and puts forward to the refine- restricted isometry property,but he does not give the relationship of incoherent constant and r- restricted isometry constant.The theorem 3 in this paper provides value relationship between them,effectively promotes the study of matrix completion.This paper introduces several kinds of algorithms commonly used in matrix completion,and the subsequent simulation compares the reconstruction performance of these algorithms in detail.

关 键 词：稀疏约束 矩阵填充 重构算法 

分 类 号：O151.21[理学—数学]