Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space
Due to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in Sobolev space HsR. We obtain the sufficient and ne...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/9932668 |
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| _version_ | 1849305511649869824 |
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| author | Hui-Min Liu Yu Tian |
| author_facet | Hui-Min Liu Yu Tian |
| author_sort | Hui-Min Liu |
| collection | DOAJ |
| description | Due to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in Sobolev space HsR. We obtain the sufficient and necessary conditions for IWS and IGS to be frames. By applying these conditions, we also derive the characterizations of IWS and IGS to be frames. Finally, we discuss the perturbation theorem of irregular wavelet frames (IWFs) and irregular Gabor frames (IGFs). We also provided some examples to support our results. |
| format | Article |
| id | doaj-art-0156ef36f8bf40a4a74b131f7aee59fd |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0156ef36f8bf40a4a74b131f7aee59fd2025-08-20T03:55:27ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/9932668Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev SpaceHui-Min Liu0Yu Tian1College of Basic ScienceDepartment of Mathematics and Information ScienceDue to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in Sobolev space HsR. We obtain the sufficient and necessary conditions for IWS and IGS to be frames. By applying these conditions, we also derive the characterizations of IWS and IGS to be frames. Finally, we discuss the perturbation theorem of irregular wavelet frames (IWFs) and irregular Gabor frames (IGFs). We also provided some examples to support our results.http://dx.doi.org/10.1155/2024/9932668 |
| spellingShingle | Hui-Min Liu Yu Tian Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space Journal of Mathematics |
| title | Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space |
| title_full | Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space |
| title_fullStr | Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space |
| title_full_unstemmed | Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space |
| title_short | Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space |
| title_sort | some conditions and perturbation theorem of irregular wavelet gabor frames in sobolev space |
| url | http://dx.doi.org/10.1155/2024/9932668 |
| work_keys_str_mv | AT huiminliu someconditionsandperturbationtheoremofirregularwaveletgaborframesinsobolevspace AT yutian someconditionsandperturbationtheoremofirregularwaveletgaborframesinsobolevspace |