Nonseparable multivariate wavelets

dc.contributor.advisor Fritz Keinert Bhatt, Ghan
dc.contributor.department Mathematics 2018-08-24T22:24:56.000 2020-06-30T07:13:00Z 2020-06-30T07:13:00Z Thu Jan 01 00:00:00 UTC 2004 2004-01-01
dc.description.abstract <p>We review the one-dimensional setting of wavelet theory and generalize it to nonseparable multivariate wavelets. This process presents significant technical difficulties. Some techniques of the one-dimensional setting carry over in a more or less straightforward way; some do not generalize at all.;The main results include the following: an algorithm for computing the moments for multivariate multiwavelets; a necessary and sufficient condition for the approximation order; the lifting scheme for multivariate wavelets; and a generalization of the method of Lai [12] for the biorthogonal completion of a polyphase matrix under suitable conditions.;One-dimensional techniques which cannot be generalized include the factorization of the polyphase matrix, and a general solution to the completion problem.</p>
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dc.identifier archive/
dc.identifier.articleid 2144
dc.identifier.contextkey 6090579
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/1145
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 18:50:27 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Mathematics
dc.subject.keywords Applied mathematics
dc.title Nonseparable multivariate wavelets
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 dissertation Doctor of Philosophy
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