Log-Sum Regularized Kaczmarz Algorithms for High-Order Tensor Recovery
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914762536779776 |
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| author | Henneberger, Katherine Qin, Jing |
| author_facet | Henneberger, Katherine Qin, Jing |
| contents | Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their convex relaxed versions are typically adopted in practice due to the computational efficiency, e.g., log-sum penalty. In this work, we propose novel log-sum regularized Kaczmarz algorithms for recovering high-order tensors with either sparse or low-rank structures. We present block variants along with convergence analysis of the proposed algorithms. Numerical experiments on synthetic and real-world data sets demonstrate the effectiveness of the proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00783 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Log-Sum Regularized Kaczmarz Algorithms for High-Order Tensor Recovery Henneberger, Katherine Qin, Jing Optimization and Control Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their convex relaxed versions are typically adopted in practice due to the computational efficiency, e.g., log-sum penalty. In this work, we propose novel log-sum regularized Kaczmarz algorithms for recovering high-order tensors with either sparse or low-rank structures. We present block variants along with convergence analysis of the proposed algorithms. Numerical experiments on synthetic and real-world data sets demonstrate the effectiveness of the proposed methods. |
| title | Log-Sum Regularized Kaczmarz Algorithms for High-Order Tensor Recovery |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2311.00783 |