Partial parameterization of orthogonal wavelet matrix filters
- In this paper we propose a procedure which allows the construction of a large family of FIR d x d matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts by two. A characterization of the class of filters of full rank type that can be obtained with such procedure is given. In particular, we restrict our attention to a special construction based on the representation of SO(2d) in terms of the elements of its Lie algebra. Explicit expressions for the filters in the case d = 2 are given, as a result of a local analysis of the parameterization obtained from perturbing the Haar system.
Author details: | Mariantonia Cotronei, Matthias HolschneiderORCiDGND |
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DOI: | https://doi.org/10.1016/j.cam.2012.11.016 |
ISSN: | 0377-0427 |
Title of parent work (English): | Journal of computational and applied mathematics |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Year of first publication: | 2013 |
Publication year: | 2013 |
Release date: | 2017/03/26 |
Tag: | Full rank matrix filters; Multichannel wavelets; Quadrature mirror filters; Vector subdivision schemes |
Volume: | 243 |
Issue: | 4 |
Number of pages: | 13 |
First page: | 113 |
Last Page: | 125 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |