Scalable frames

被引：52

作者：

Kutyniok, Gitta ^{[1
]}

Okoudjou, Kasso A. ^{[2
]}

Philipp, Friedrich ^{[1
]}

Tuley, Elizabeth K. ^{[3
]}

机构：

[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[3] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 05期

关键词：

Conical surfaces; Diagonal operator; Preconditioner; Tight frames;

D O I：

10.1016/j.laa.2012.10.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process which can also be regarded as perfect preconditioning of a frame by a diagonal operator. A frame is called scalable, if such a diagonal operator exists. We derive various characterizations of scalable frames, thereby including the infinite-dimensional situation. Finally, we provide a geometric interpretation of scalability in terms of conical surfaces. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：2225 / 2238

页数：14

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