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Wavelets with integer dilation facto...

Arizona State University.

Wavelets with integer dilation factors larger than two.

レコード種別:	コンピュータ・メディア : 単行資料
タイトル / 著者:	Wavelets with integer dilation factors larger than two./
著者:	Boerner, Rochus.
記述:	143 p.
注記:	Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0775.
含まれています:	Dissertation Abstracts International65-02B.
主題:	Mathematics. -
電子資源:	Download fulltext (下載全文)
国際標準図書番号 (ISBN):	0496708333

Wavelets with integer dilation factors larger than two.
Boerner, Rochus.

Wavelets with integer dilation factors larger than two. - 143 p.

Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0775.

Thesis (Ph.D.)--Arizona State University, 2004.

The theory of dyadic multiresolution analyses and wavelets on the real line is extended to arbitrary integer dilations a > 1. The notion of a multiresolution analysis (MRA) with dilation factor a is defined in the obvious way; the well-known theorems that describe the relationship between the scaling function, the low-pass filter and the MRA are generalized. The difference spaces Wj are characterized, and the already known result, that a-1 wavelets are required to generate W0, is re-derived. A constructive proof is developed that these a-1 wavelets always exist, consisting of an explicit formula for the a-1 high-pass filters. The wavelet decomposition algorithm is extended to cover the case of a general a. It is shown how to create multiresolution analyses in n dimensions from the one dimensional MRA.

ISBN: 0496708333Subjects--Topical Terms:

146772
Mathematics.

Wavelets with integer dilation factors larger than two.
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245 1 0 $a Wavelets with integer dilation factors larger than two.
300 $a 143 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0775.
500 $a Adviser: Anne Gelb.
502 $a Thesis (Ph.D.)--Arizona State University, 2004.
520 $a The theory of dyadic multiresolution analyses and wavelets on the real line is extended to arbitrary integer dilations a > 1. The notion of a multiresolution analysis (MRA) with dilation factor a is defined in the obvious way; the well-known theorems that describe the relationship between the scaling function, the low-pass filter and the MRA are generalized. The difference spaces Wj are characterized, and the already known result, that a-1 wavelets are required to generate W0, is re-derived. A constructive proof is developed that these a-1 wavelets always exist, consisting of an explicit formula for the a-1 high-pass filters. The wavelet decomposition algorithm is extended to cover the case of a general a. It is shown how to create multiresolution analyses in n dimensions from the one dimensional MRA.
520 $a Continuous, compactly supported scaling functions and wavelets are constructed and an improved technique for estimating their regularity is developed. Some scaling functions and wavelets are computed numerically for the case a = 3 and a = 4. An application to image coding is considered.
590 $a School code: 0010.
650 4 $a Mathematics. $3 146772
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710 2 0 $a Arizona State University. $3 1000005534
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790 1 0 $a Gelb, Anne, $e advisor
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791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3123522 $z Download fulltext (下載全文)