Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators
For any dilation matrix with integer entries and , we construct a family of smooth compactly supported tight wavelet frames with three generators in . Our construction involves some compactly supported refinable functions, the oblique extension principle, and a slight generalization of a theorem of...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/818907 |
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| author | A. San Antolín R. A. Zalik |
| author_facet | A. San Antolín R. A. Zalik |
| author_sort | A. San Antolín |
| collection | DOAJ |
| description | For any dilation matrix with integer entries and , we construct a family of smooth compactly supported tight wavelet frames with three generators in . Our construction involves some compactly supported refinable functions, the oblique extension principle, and a slight generalization of a theorem of Lai and Stöckler. Estimates for the degrees of smoothness are given. With the exception of a polynomial whose coefficients must in general be computed by spectral factorization, the framelets are expressed in closed form in the frequency domain, in terms of elementary transcendental functions. By means of two examples we also show that for low degrees of smoothness the use of spectral factorization may be avoided. |
| format | Article |
| id | doaj-art-2e5abb046ebe4645b6a44243d65ee928 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2e5abb046ebe4645b6a44243d65ee9282025-02-03T05:53:57ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/818907818907Some Bivariate Smooth Compactly Supported Tight Framelets with Three GeneratorsA. San Antolín0R. A. Zalik1Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, SpainDepartment of Mathematics and Statistics, Auburn University, Auburn, AL 36849-5310, USAFor any dilation matrix with integer entries and , we construct a family of smooth compactly supported tight wavelet frames with three generators in . Our construction involves some compactly supported refinable functions, the oblique extension principle, and a slight generalization of a theorem of Lai and Stöckler. Estimates for the degrees of smoothness are given. With the exception of a polynomial whose coefficients must in general be computed by spectral factorization, the framelets are expressed in closed form in the frequency domain, in terms of elementary transcendental functions. By means of two examples we also show that for low degrees of smoothness the use of spectral factorization may be avoided.http://dx.doi.org/10.1155/2013/818907 |
| spellingShingle | A. San Antolín R. A. Zalik Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators Abstract and Applied Analysis |
| title | Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators |
| title_full | Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators |
| title_fullStr | Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators |
| title_full_unstemmed | Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators |
| title_short | Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators |
| title_sort | some bivariate smooth compactly supported tight framelets with three generators |
| url | http://dx.doi.org/10.1155/2013/818907 |
| work_keys_str_mv | AT asanantolin somebivariatesmoothcompactlysupportedtightframeletswiththreegenerators AT razalik somebivariatesmoothcompactlysupportedtightframeletswiththreegenerators |