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

摘要

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