In this chapter we give an overview of a method recently developed for designing wavelet filter banks via the Quillen-Suslin Theorem for Laurent polynomials. In this method, the Quillen-Suslin Theorem is used to transform vectors with Laurent polynomial entries to other vectors with Laurent polynomial entries so that the matrix analysis tools that were not readily available for the vectors before the transformation can now be employed. As a result, a powerful and general method for designing non-redundant wavelet filter banks is obtained. In particular, the vanishing moments of the resulting wavelet filter banks can be controlled in a very simple way, which is especially advantageous compared to other existing methods for the multi-dimensional cases.
|Title of host publication||Applied and Numerical Harmonic Analysis|
|Publisher||Springer International Publishing|
|Number of pages||11|
|Publication status||Published - 2017|
|Name||Applied and Numerical Harmonic Analysis|
Bibliographical noteFunding Information:
*This chapter is mainly based on the work with Hyungju Park and Fang Zheng presented in . This research was partially supported by National Research Foundation of Korea (NRF) Grants 20151003262 and 20151009350.
All Science Journal Classification (ASJC) codes
- Applied Mathematics