Tight Wavelet Filter Banks with Prescribed Directions

TL;DR

This paper introduces a systematic method for designing tight wavelet filter banks with any prescribed directions, multi-dimensional applicability, and customizable vanishing moments, along with efficient analysis and synthesis algorithms.

Contribution

It provides a novel construction approach for directional tight wavelet filter banks with flexible properties and practical algorithms.

Findings

Supports any multi-dimensional setting

Allows prescribed number of vanishing moments

Includes fast analysis and synthesis algorithms

Abstract

Constructing tight wavelet filter banks with prescribed directions is challenging. This paper presents a systematic method for designing a tight wavelet filter bank, given any prescribed directions. There are two types of wavelet filters in our tight wavelet filter bank. One type is entirely determined by the prescribed information about the directionality and makes the wavelet filter bank directional. The other type helps the wavelet filter bank to be tight. In addition to the flexibility in choosing the directions, our construction method has other useful properties. It works for any multi-dimension, and it allows the user to have any prescribed number of vanishing moments along the chosen directions. Furthermore, our tight wavelet filter banks have fast algorithms for analysis and synthesis. Concrete examples are given to illustrate our construction method and properties of resulting tight wavelet filter banks.