Decay properties of restricted isometry constants

被引：17

作者：

Blanchard, Jeffey D. ^{[1
]}

Cartis, Coralia ^{[2
]}

Tanner, Jared ^{[2
]}

机构：

[1] Department of Mathematics, University of Utah, Salt Lake City

[2] School of Mathematics and the Maxwell Institute, University of Edinburgh, Edinburgh

来源：

IEEE Signal Processing Letters | 2009年 / 16卷 / 07期

关键词：

Compressed sensing; Restricted isometry constants; RIP; Sparse approximation;

D O I：

10.1109/LSP.2009.2020882

中图分类号：

学科分类号：

摘要：

Many sparse approximation algorithms accurately recover the sparsest solution to an underdetermined system of equations provided the matrix's restricted isometry constants (RICs) satisfy certain bounds. There are no known large deterministic matrices that satisfy the desired RIC bounds; however, members of many random matrix ensembles typically satisfy RIC bounds. This experience with random matrices has colored the view of the RICs' behavior. By modifying matrices assumed to have bounded RICs, we construct matrices whose RICs behave in a markedly different fashion than the classical random matrices; RICs can satisfy desirable bounds and also take on values in a narrow range. © 2009 IEEE.

引用

页码：572 / 575

页数：3

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