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arXiv · 1407.5513

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

Youngmi Hur·Fang Zheng
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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 whom 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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BibTeXRIS

Youngmi Hur, Fang Zheng. 2014-07-21. Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks with Fast Algorithms. https://arxiv.org/abs/1407.5513

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