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   -> Volume 11, Issue 1

Preprint: The Phaselet Transform
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Ramesh Gopinath (

PostPosted: Mon Jan 07, 2002 10:21 am    
Subject: Preprint: The Phaselet Transform
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Here is a preprint of a paper submitted to IEEE Trans. in Signal Processing, December 2000.

Author: Ramesh A. Gopinath

Title: The Phaselet Transform - An Integral Redundancy Nearly Shift-Invariant Wavelet Transform

This paper introduces an approximately shift invariant redundant dyadic wavelet transform - the phaselet transform - that includes the popular dual-tree complex wavelet transform of Kingsbury \cite{Kingsbury-dual-tree} as a special case. The main idea is to use a finite set of wavelets that related to each other in a special way - and hence called phaselets - to achieve approximate shift-redundancy; bigger the set better the approximation. A sufficient condition on the associated scaling filters to achieve this is that they are fractional shifts of each other. Algorithms for the design of of phaselets with a fixed number vanishing moments is presented - building upon the work of Selesnick \cite{Selesnick-hilbert-design} for the design of wavelet pairs for Kingsbury's dual-tree complex wavelet transform. Construction of 2-dimensional directional bases from tensor products of 1-d phaselets is also described.

Available at sp2001.pdf

Dr. Ramesh A. Gopinath
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