A note on the standard dual frame of a wavelet frame with three-scale☆

2009 ◽  
Vol 42 (2) ◽  
pp. 931-937 ◽  
Author(s):  
Qingjiang Chen ◽  
Zongtian Wei ◽  
Jinshun Feng
Keyword(s):  
Dual Frame ◽  
Wavelet Frame

Constructing totally interpolating wavelet frame systems

2015 ◽  
Vol 13 (03) ◽  
pp. 1550017
Author(s):  
Baobin Li
Keyword(s):  
Filter Banks ◽  
Scaling Function ◽  
Tight Frame ◽  
Special Structure ◽  
Dual Frame ◽  
Wavelet Frame ◽  
Continuous Linear ◽  
Wavelet Frames ◽  
Frame Systems ◽  
The Scaling Function

The system of totally interpolating wavelet frames is discussed in this paper, in which both the scaling function and one of wavelet functions are interpolating. It will be shown that corresponding filter banks possess the special structure, and the parametrization of filter banks is present. Moreover, we show that when considering tight frame systems with two generators, the Ron–Shen's continuous-linear-spline-based tight frame is the only one with totally interpolating property and symmetry. But in the dual frame context, more good examples of bi-frames with symmetric/antisymmetric property can be obtained and constructed, which in particular, include frames with the uniform symmetry.

Study of Periodic Frames and Trivariate Tight Wavelet Frames and Applications in Materials Engineering

2014 ◽  
Vol 1079-1080 ◽  
pp. 878-881
Author(s):  
Song Zhen Sun ◽  
Yi Guo
Keyword(s):  
Time Domain ◽  
Dual Frame ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Materials Engineering ◽  
Number Of Generators ◽  
Dual Wavelet Frames ◽  
The Time Domain ◽  
Dual Wavelet

It is shown that there exists a frame wavelet with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions.

scholarly journals The Canonical Dual Frame of a Wavelet Frame

2002 ◽  
Vol 12 (3) ◽  
pp. 269-285 ◽  
Author(s):  
Ingrid Daubechies ◽  
Bin Han
Keyword(s):  
Dual Frame ◽  
Wavelet Frame

On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle

2014 ◽  
Vol 57 (2) ◽  
pp. 254-263 ◽  
Author(s):  
Ole Christensen ◽  
Hong Oh Kim ◽  
Rae Young Kim
Keyword(s):  
Extension Principle ◽  
Sufficient Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Number Of Generators ◽  
Unitary Extension

AbstractThe unitary extension principle (UEP) by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.

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