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
相关论文
共 50 条
  • [41] IRREGULAR WAVELET FRAMES AND GABOR FRAMES
    Ole Christensen
    Approximation Theory and Its Applications, 2001, (03) : 90 - 100
  • [42] ON THE STABILITY OF FUSION FRAMES (FRAMES OF SUBSPACES)
    Asgari, Mohammad Sadegh
    ACTA MATHEMATICA SCIENTIA, 2011, 31 (04) : 1633 - 1642
  • [43] Frames and Dual Frames for Krein Spaces
    Li, Yun-Zhang
    Dong, Rui-Qi
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2024, 45 (4-6) : 355 - 372
  • [44] Partial Gabor frames and dual frames
    Tian, Yu
    Jia, Hui-Fang
    He, Guo-Liang
    INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2022, 20 (01)
  • [45] CONTINUOUS FRAMES AND G-FRAMES
    Avazzadeh, S. H.
    Kamyabi-Gol, R. A.
    Tousi, R. Raisi
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2014, 40 (04) : 1047 - 1055
  • [46] 'FRAMES'
    SORESCU, M
    SALMAGUNDI-A QUARTERLY OF THE HUMANITIES AND SOCIAL SCIENCES, 1993, (98-99): : 83 - 83
  • [47] 'FRAMES'
    WERNERKING, J
    ARIEL-A REVIEW OF INTERNATIONAL ENGLISH LITERATURE, 1986, 17 (04) : 48 - 48
  • [48] Frames
    Schmidt, Gunther
    Winter, Michael
    RELATIONAL TOPOLOGY, 2018, 2208 : 145 - 153
  • [49] 'FRAMES'
    RICE, S
    ARTFORUM, 1980, 18 (10): : 88 - 89
  • [50] Frames
    Sallis, John
    COMPARATIVE AND CONTINENTAL PHILOSOPHY, 2020, 12 (03) : 245 - 253
12345