Multifilters with and without Prefilters |
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Authors: | S. Bacchelli M. Cotronei T. Sauer |
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Affiliation: | (1) Department of Mathematics, University of Bologna, Piazza di Porta S. Donato, 5, IT-40127 Bologna, Italy;(2) Department of Mathematics, University of Messina, Salita Sperone, 31, IT-98166 Messina, Italy;(3) Lehrstuhl für Numerische Mathematik, Justus-Liebig-Universtät Gieen, Heinrich-Buff-Ring 44, DE-35392 Gieen, Germany |
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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. The construction of such filters via the lifting scheme is pointed out and examples of the performance of these filters for image compression are given. |
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Keywords: | Full rank multifilters prefiltering approximation order lifting scheme biorthogonal filters |
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