Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks with Fast Algorithms

Youngmi Hur; Fang Zheng

doi:10.1109/TIT.2016.2608896

Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks with Fast Algorithms

Youngmi Hur, Fang Zheng

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

As constructing multi-D wavelets remains a challenging problem, we propose a new method called prime coset sum to construct multi-D wavelets. Our method provides a systematic way to construct multi-D non-separable wavelet filter banks from two 1-D lowpass filters, with one of which being interpolatory. Our method has many important features including the following: 1) it works for any spatial dimension, and any prime scalar dilation, 2) the vanishing moments of the multi-D wavelet filter banks are guaranteed by certain properties of the initial 1-D lowpass filters, and furthermore, 3) the resulting multi-D wavelet filter banks are associated with fast algorithms that are faster than the existing fast tensor product algorithms.

Original language	English
Article number	7565569
Journal	IEEE Transactions on Information Theory
Volume	PP
Issue number	99
DOIs	https://doi.org/10.1109/TIT.2016.2608896
Publication status	Published - 2016

Bibliographical note

Funding Information:
This research was supported in part by Yonsei New Faculty Research Seed Money Grant, National Research Foundation of Korea (NRF) Grants 20151003262 and 20151009350, and NSF Grant DMS-1115870.

Publisher Copyright:
© 2016 IEEE.

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2016.2608896

Cite this

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abstract = "As constructing multi-D wavelets remains a challenging problem, we propose a new method called prime coset sum to construct multi-D wavelets. Our method provides a systematic way to construct multi-D non-separable wavelet filter banks from two 1-D lowpass filters, with one of which being interpolatory. Our method has many important features including the following: 1) it works for any spatial dimension, and any prime scalar dilation, 2) the vanishing moments of the multi-D wavelet filter banks are guaranteed by certain properties of the initial 1-D lowpass filters, and furthermore, 3) the resulting multi-D wavelet filter banks are associated with fast algorithms that are faster than the existing fast tensor product algorithms.",

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Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks with Fast Algorithms

Abstract

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