A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting
In some applications, there are signals with a piecewise structure to be recovered. In this paper, we propose a piecewise sparse approximation model and a piecewise proximal gradient method (JPGA) which aim to approximate piecewise signals. We also make an analysis of the JPGA based on differential...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2022-12-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.34768/amcs-2022-0046 |
| _version_ | 1811171356107079680 |
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| author | Zhong Yijun Li Chongjun Li Zhong Duan Xiaojuan |
| author_facet | Zhong Yijun Li Chongjun Li Zhong Duan Xiaojuan |
| author_sort | Zhong Yijun |
| collection | DOAJ |
| description | In some applications, there are signals with a piecewise structure to be recovered. In this paper, we propose a piecewise sparse approximation model and a piecewise proximal gradient method (JPGA) which aim to approximate piecewise signals. We also make an analysis of the JPGA based on differential equations, which provides another perspective on the convergence rate of the JPGA. In addition, we show that the problem of sparse representation of the fitting surface to the given scattered data can be considered as a piecewise sparse approximation. Numerical experimental results show that the JPGA can not only effectively fit the surface, but also protect the piecewise sparsity of the representation coefficient. |
| first_indexed | 2024-04-10T17:12:37Z |
| format | Article |
| id | doaj.art-28c85892611b454b8b96b4b8e08ae0a9 |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-04-10T17:12:37Z |
| publishDate | 2022-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-28c85892611b454b8b96b4b8e08ae0a92023-02-05T19:21:10ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922022-12-0132467168210.34768/amcs-2022-0046A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data FittingZhong Yijun0Li Chongjun1Li Zhong2Duan Xiaojuan3Department of Mathematical Sciences, Zhejiang Sci-Tech University, No. 928, No. 2 Street, Xiasha Higher Education Park, Hangzhou, ChinaSchool of Mathematical Sciences, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, ChinaDepartment of Science and Technology, Huzhou University, 759 Erhuan East Road, Huzhou, ChinaDepartment of Mathematical Sciences, Zhejiang Sci-Tech University, No. 928, No. 2 Street, Xiasha Higher Education Park, Hangzhou, ChinaIn some applications, there are signals with a piecewise structure to be recovered. In this paper, we propose a piecewise sparse approximation model and a piecewise proximal gradient method (JPGA) which aim to approximate piecewise signals. We also make an analysis of the JPGA based on differential equations, which provides another perspective on the convergence rate of the JPGA. In addition, we show that the problem of sparse representation of the fitting surface to the given scattered data can be considered as a piecewise sparse approximation. Numerical experimental results show that the JPGA can not only effectively fit the surface, but also protect the piecewise sparsity of the representation coefficient.https://doi.org/10.34768/amcs-2022-0046piecewise sparse approximationproximal gradientscattered data fitting |
| spellingShingle | Zhong Yijun Li Chongjun Li Zhong Duan Xiaojuan A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting International Journal of Applied Mathematics and Computer Science piecewise sparse approximation proximal gradient scattered data fitting |
| title | A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting |
| title_full | A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting |
| title_fullStr | A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting |
| title_full_unstemmed | A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting |
| title_short | A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting |
| title_sort | proximal based algorithm for piecewise sparse approximation with application to scattered data fitting |
| topic | piecewise sparse approximation proximal gradient scattered data fitting |
| url | https://doi.org/10.34768/amcs-2022-0046 |
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