Bi-orthogonal Directional Wavelet Bases: Regularity and Numerical Construction
Rujie Yin · arXiv (Cornell University) · 2016
In this report, we consider the regularity of bi-orthogonal directional wavelet bases with dilated quincunx subsampling. This work is an extension of the orthonormal setup considered earlier by the author, where it is shown that orthonormal directional wavelets built on dilated quincunx lattice cannot have smooth frequency support and this irregularity can be removed in a frame construction with redundancy factor of 2. Here, the same irregularity arises in our analysis of bi-orthogonal construction, which is different from the previous analysis of orthonormal bases, based on a numerical algorithm introduced by Cohen et al for constructing compactly supported symmetric wavelet bases on hexagonal lattice. We extend and adapt this algorithm to our framework.