The canonical dual frame of a wavelet frame

被引:57
作者
Daubechies, I [1 ]
Han, B [1 ]
机构
[1] Princeton Univ, Dept Math, PACM, Princeton, NJ 08544 USA
基金
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词
wavelet frame; the canonical dual frame; dual wavelet frame;
D O I
10.1006/acha.2002.0381
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we show that there exist wavelet frames that have nice dual wavelet frames, but for which the canonical dual frame does not consist of wavelets, i.e., cannot be generated by the translates and dilates of a single function. (C) 2002 Elsevier Science (USA).
引用
收藏
页码:269 / 285
页数:17
相关论文
共 8 条
[1]   INEQUALITIES OF LITTLEWOOD-PALEY TYPE FOR FRAMES AND WAVELETS [J].
CHUI, CK ;
SHI, XL .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (01) :263-277
[2]   THE WAVELET TRANSFORM, TIME-FREQUENCY LOCALIZATION AND SIGNAL ANALYSIS [J].
DAUBECHIES, I .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1990, 36 (05) :961-1005
[3]  
DAUBECHIES I, 1992, CBMS NSF REGIONAL C, V61
[4]  
DAUBECHIES I, IN PRESS CONSTR APPR
[5]   A CLASS OF NONHARMONIC FOURIER SERIES [J].
DUFFIN, RJ ;
SCHAEFFER, AC .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 72 (MAR) :341-366
[6]   On dual wavelet tight frames [J].
Han, B .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1997, 4 (04) :380-413
[7]  
Naimark M. A., 1959, NORMED RINGS
[8]   Affine systems in L-2(R-d) .2. Dual systems [J].
Ron, A ;
Shen, ZW .
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1997, 3 (05) :617-637