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.
|Journal||International Journal of Wavelets, Multiresolution and Information Processing|
|Publication status||Published - 2022 Jul 1|
Bibliographical noteFunding Information:
This work was supported in part by the National Research Foundation of Korea (NRF) Grant Nos. [2015R1A5A1009350 and 2021R1A2C1007598] and in part by the Institute of Information & Communications Technology Planning & Evaluation (IITP) Grant No. [2021-0-00023], both funded by the Korea government (MSIT). Part of the work was performed while the author was visiting the Korea Institute for Advanced Study, Seoul, Korea.
© 2022 World Scientific Publishing Company.
All Science Journal Classification (ASJC) codes
- Signal Processing
- Information Systems
- Applied Mathematics