  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.
