Source:http://linkedlifedata.com/resource/pubmed/id/20028635
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| Predicate | Object |
|---|---|
| rdf:type | |
| lifeskim:mentions | |
| pubmed:issue |
3
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| pubmed:dateCreated |
2010-2-22
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| pubmed:abstractText |
In this paper, we present the lifting scheme of wavelet bi-frames along with theory analysis, structure, and algorithm. We show how any wavelet bi-frame can be decomposed into a finite sequence of simple filtering steps. This decomposition corresponds to a factorization of a polyphase matrix of a wavelet bi-frame. Based on this concept, we present a new idea for constructing wavelet bi-frames. For the construction of symmetric bi-frames, we use generalized Bernstein basis functions, which enable us to design symmetric prediction and update filters. The construction allows more efficient implementation and provides tools for custom design of wavelet bi-frames. By combining the different designed filters for the prediction and update steps, we can devise practically unlimited forms of wavelet bi-frames. Moreover, we present an algorithm of increasing the number of vanishing moments of bi-framelets to arbitrary order via the presented lifting scheme, which adopts an iterative algorithm and ensures the shortest lifting scheme. Several construction examples are given to illustrate the results.
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| pubmed:language |
eng
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| pubmed:journal | |
| pubmed:status |
PubMed-not-MEDLINE
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| pubmed:month |
Mar
|
| pubmed:issn |
1941-0042
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| pubmed:author | |
| pubmed:issnType |
Electronic
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| pubmed:volume |
19
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| pubmed:owner |
NLM
|
| pubmed:authorsComplete |
Y
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| pubmed:pagination |
612-24
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| pubmed:year |
2010
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| pubmed:articleTitle |
The lifting scheme for wavelet bi-frames: theory, structure, and algorithm.
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| pubmed:affiliation |
Key Laboratory of Mathematics, Informatics, and Behavioral Semantics, Ministry of Education, China. xiaoyuanyang@vip.163.com
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| pubmed:publicationType |
Journal Article,
Research Support, Non-U.S. Gov't
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