Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters
Due to the difficulty for constructing two-dimensional wavelet filters, the commonly used wavelet filters are tensor-product of one-dimensional wavelet filters. In some applications, more perfect reconstruction filters should be provided. In this paper, we introduce a transformation which is referre...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/272801 |
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| _version_ | 1832558116536844288 |
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| author | Fei Li Jianwei Yang |
| author_facet | Fei Li Jianwei Yang |
| author_sort | Fei Li |
| collection | DOAJ |
| description | Due to the difficulty for constructing two-dimensional wavelet filters, the commonly used wavelet filters are tensor-product of one-dimensional wavelet filters. In some applications, more perfect reconstruction filters should be provided. In this paper, we introduce a transformation which is referred to as Shift Unitary Transform (SUT) of Conjugate Quadrature Filter (CQF). In terms of this transformation, we propose a parametrization method for constructing two-dimensional orthogonal wavelet filters. It is proved that tensor-product wavelet filters are only special cases of this parametrization method. To show this, we introduce the SUT of one-dimensional CQF and present a complete parametrization of one-dimensional wavelet system. As a result, more ways are provided to randomly generate two-dimensional perfect reconstruction filters. |
| format | Article |
| id | doaj-art-93837061af614d7e9583bf15505849f3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-93837061af614d7e9583bf15505849f32025-02-03T01:33:13ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/272801272801Shift Unitary Transform for Constructing Two-Dimensional Wavelet FiltersFei Li0Jianwei Yang1School of Economics, Beijing Technology and Business University, Beijing 100048, ChinaCollege of Math and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaDue to the difficulty for constructing two-dimensional wavelet filters, the commonly used wavelet filters are tensor-product of one-dimensional wavelet filters. In some applications, more perfect reconstruction filters should be provided. In this paper, we introduce a transformation which is referred to as Shift Unitary Transform (SUT) of Conjugate Quadrature Filter (CQF). In terms of this transformation, we propose a parametrization method for constructing two-dimensional orthogonal wavelet filters. It is proved that tensor-product wavelet filters are only special cases of this parametrization method. To show this, we introduce the SUT of one-dimensional CQF and present a complete parametrization of one-dimensional wavelet system. As a result, more ways are provided to randomly generate two-dimensional perfect reconstruction filters.http://dx.doi.org/10.1155/2011/272801 |
| spellingShingle | Fei Li Jianwei Yang Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters Journal of Applied Mathematics |
| title | Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters |
| title_full | Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters |
| title_fullStr | Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters |
| title_full_unstemmed | Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters |
| title_short | Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters |
| title_sort | shift unitary transform for constructing two dimensional wavelet filters |
| url | http://dx.doi.org/10.1155/2011/272801 |
| work_keys_str_mv | AT feili shiftunitarytransformforconstructingtwodimensionalwaveletfilters AT jianweiyang shiftunitarytransformforconstructingtwodimensionalwaveletfilters |