scholarly journals Framelets with Three Generator by Unitary Extension Principle

2020 ◽  
Vol 9 (4) ◽  
pp. 6127-6133
Author(s):  
Kanchan Lata Gupta
Keyword(s):  
Extension Principle ◽  
Unitary Extension

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.

scholarly journals Unitary Extension Principle for Nonuniform Wavelet Frames in L2(ℝ)

2021 ◽  
Vol 17 (1) ◽  
pp. 79-94
Author(s):  
Hari Krishan Malhotra ◽  
◽  
Lalit Kumar Vashisht ◽  
Keyword(s):  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension

The Study of Tight Periodic Wavelet Frames and Wavelet Frame Packets and Applications

2014 ◽  
Vol 977 ◽  
pp. 532-535
Author(s):  
Qing Jiang Chen ◽  
Yu Zhou Chai ◽  
Chuan Li Cai
Keyword(s):  
Information Science ◽  
Approximation Order ◽  
Tight Frame ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Periodic Wavelet ◽  
Unitary Extension ◽  
Periodic Wavelet Frames ◽  
Necessary And Sufficient

Information science focuses on understanding problems from the perspective of the stake holders involved and then applying information and other technologies as needed. A necessary and sufficient condition is identified in term of refinement masks for applying the unitary extension principle for periodic functions to construct tight wavelet frames. Then a theory on the approxi-mation order of truncated tight frame series is established, which facilitates construction of tight periodic wavelet frames with desirable approximation order. The pyramid decomposition scheme is derived based on the generalized multiresolution structure.

scholarly journals Polyphase matrix characterization of framelets on local fields of positive characteristic

2017 ◽  
Vol 9 (1) ◽  
pp. 248-259
Author(s):  
F. A. Shah ◽  
M. Y. Bhat
Keyword(s):  
Positive Characteristic ◽  
Local Fields ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension ◽  
Polyphase Matrix

AbstractAn important tool for the construction of framelets on local fields of positive characteristic using unitary extension principle was presented by Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293-307]. In this article, we continue the study of framelets on local fields and present a polyphase matrix characterization of framelets generated by the extension principle.

GMRA-BASED CONSTRUCTION OF FRAMELETS IN REDUCING SUBSPACES OF L2(ℝd)

2011 ◽  
Vol 09 (02) ◽  
pp. 237-268 ◽  
Author(s):  
YUN-ZHANG LI ◽  
FENG-YING ZHOU
Keyword(s):  
Explicit Construction ◽  
Extension Principle ◽  
Reducing Subspaces ◽  
Unitary Extension ◽  
Expansive Matrix

This paper develops GMRA-based construction procedures of Parseval framelets in the setting of reducing subspaces of L2(ℝd). A unitary extension principle is established; in particular, for a general expansive matrix A with | det A| = 2, an explicit construction of Parseval framelets is obtained. Some examples are also provided to illustrate the generality of our theory.

Dual Gramian analysis: Duality principle and unitary extension principle

2015 ◽  
Vol 85 (297) ◽  
pp. 239-270 ◽  
Author(s):  
Zhitao Fan ◽  
Hui Ji ◽  
Zuowei Shen
Keyword(s):  
Duality Principle ◽  
Extension Principle ◽  
Unitary Extension ◽  
Dual Gramian

CONSTRUCTION OF SYMMETRIC TIGHT WAVELET FRAMES FROM QUASI-INTERPOLATORY SUBDIVISION MASKS AND THEIR APPLICATIONS

2008 ◽  
Vol 06 (01) ◽  
pp. 97-120 ◽  
Author(s):  
BYEONGSEON JEONG ◽  
MYUNGJIN CHOI ◽  
HONG OH KIM
Keyword(s):  
Filter Bank ◽  
Extension Principle ◽  
Discrete Wavelet ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Vanishing Moments ◽  
Frequency Scale ◽  
Unitary Extension ◽  
Signal Image ◽  
Interpolatory Subdivision

This paper presents tight wavelet frames with two compactly supported symmetric generators of more than one vanishing moments in the Unitary Extension Principle. We determine all possible free tension parameters of the quasi-interpolatory subdivision masks whose corresponding refinable functions guarantee our wavelet frame. In order to reduce shift variance of the standard discrete wavelet transform, we use the three times oversampling filter bank and eventually obtain a ternary (low, middle, high) frequency scale. In applications to signal/image denoising and erasure recovery, the results demonstrate reduced shift variance and better performance of our wavelet frame than the usual wavelet systems such as Daubechies wavelets.

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