Tight wavelet filter banks with prescribed directions

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 multidimension, 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.