Journal article

Publication year: 2002

Pages: 231-261

Journal: BIT Numerical Mathematics

Volume number: 42

Issue number: 2

ISSN: 0006-3835

DOI Link: https://doi.org/10.1023/A:1021990606994

Publisher: Springer

Abstract: 
To explore the full approximation order and thus compression power of a multifilter, it is usually necessary to incorporate prefilters. Using matrix factorization techniques, we describe an explicit construction of such prefilters. Although in the case of approximation order 1 these prefilters are simply bi-infinite block diagonal matrices, they can become very intricate as soon as one aims for higher approximation order. For this reason, we introduce a particular class of multifilters which we call full rank multifilters. These filters have a peculiar structure which allows us to obtain approximation order without the use of prefilters. he construction of such filters via the lifting scheme is pointed out and examples of the performance of these filters for image compression are given.

Harvard Citation style: Bacchelli, S., Cotronei, M. and Sauer, T. (2002) Multifilters with and without prefilters, BIT Numerical Mathematics, 42(2), pp. 231-261. https://doi.org/10.1023/A:1021990606994

APA Citation style: Bacchelli, S., Cotronei, M., & Sauer, T. (2002). Multifilters with and without prefilters. BIT Numerical Mathematics. 42(2), 231-261. https://doi.org/10.1023/A:1021990606994