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
收藏
页码：2225 / 2238
页数：14
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