Dual Wavelet Frame Transforms on Manifolds and Graphs
In this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the deco...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/1637623 |
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| _version_ | 1832548558712078336 |
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| author | Lihong Cui Qiaoyun Wu Jiale Liu Jianjun Sun |
| author_facet | Lihong Cui Qiaoyun Wu Jiale Liu Jianjun Sun |
| author_sort | Lihong Cui |
| collection | DOAJ |
| description | In this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the decomposition and reconstruction for the dual wavelet frame transforms on graphs. Finally, we give a numerical example to illustrate the validity of the dual wavelet frame transformation applied to the graph data. |
| format | Article |
| id | doaj-art-975d6835e7cd4aaf9906189e1b434f10 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-975d6835e7cd4aaf9906189e1b434f102025-02-03T06:13:40ZengWileyJournal of Mathematics2314-46292314-47852019-01-01201910.1155/2019/16376231637623Dual Wavelet Frame Transforms on Manifolds and GraphsLihong Cui0Qiaoyun Wu1Jiale Liu2Jianjun Sun3Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, ChinaDepartment of Mathematics, Beijing University of Chemical Technology, Beijing 100029, ChinaDepartment of Mathematics, Beijing University of Chemical Technology, Beijing 100029, ChinaCollege of Chemical Engineering, Beijing University of Chemical Technology, Beijing, 100029, ChinaIn this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the decomposition and reconstruction for the dual wavelet frame transforms on graphs. Finally, we give a numerical example to illustrate the validity of the dual wavelet frame transformation applied to the graph data.http://dx.doi.org/10.1155/2019/1637623 |
| spellingShingle | Lihong Cui Qiaoyun Wu Jiale Liu Jianjun Sun Dual Wavelet Frame Transforms on Manifolds and Graphs Journal of Mathematics |
| title | Dual Wavelet Frame Transforms on Manifolds and Graphs |
| title_full | Dual Wavelet Frame Transforms on Manifolds and Graphs |
| title_fullStr | Dual Wavelet Frame Transforms on Manifolds and Graphs |
| title_full_unstemmed | Dual Wavelet Frame Transforms on Manifolds and Graphs |
| title_short | Dual Wavelet Frame Transforms on Manifolds and Graphs |
| title_sort | dual wavelet frame transforms on manifolds and graphs |
| url | http://dx.doi.org/10.1155/2019/1637623 |
| work_keys_str_mv | AT lihongcui dualwaveletframetransformsonmanifoldsandgraphs AT qiaoyunwu dualwaveletframetransformsonmanifoldsandgraphs AT jialeliu dualwaveletframetransformsonmanifoldsandgraphs AT jianjunsun dualwaveletframetransformsonmanifoldsandgraphs |