A convexity preserving nonconvex regularization for inverse problems under non-Gaussian noise
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915476087504896 |
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| author | Yata, Wataru Kume, Keita Yamada, Isao |
| author_facet | Yata, Wataru Kume, Keita Yamada, Isao |
| contents | We propose a nonconvexly regularized convex model for linear regression problems under non-Gaussian noise. The cost function of the proposed model is designed with a possibly non-quadratic data fidelity term and a nonconvex regularizer via the generalized Moreau enhancement of a seed convex regularizer. We present sufficient conditions (i) for the cost function of the proposed model to be convex over the entire space, and (ii) for the existence of a minimizer of the proposed model. Under such conditions, we propose a proximal splitting type algorithm with guaranteed convergence to a global minimizer of the proposed model. As an application, we enhance nonconvexly a convex sparsity-promoting regularizer in a scenario of simultaneous declipping and denoising. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A convexity preserving nonconvex regularization for inverse problems under non-Gaussian noise Yata, Wataru Kume, Keita Yamada, Isao Optimization and Control We propose a nonconvexly regularized convex model for linear regression problems under non-Gaussian noise. The cost function of the proposed model is designed with a possibly non-quadratic data fidelity term and a nonconvex regularizer via the generalized Moreau enhancement of a seed convex regularizer. We present sufficient conditions (i) for the cost function of the proposed model to be convex over the entire space, and (ii) for the existence of a minimizer of the proposed model. Under such conditions, we propose a proximal splitting type algorithm with guaranteed convergence to a global minimizer of the proposed model. As an application, we enhance nonconvexly a convex sparsity-promoting regularizer in a scenario of simultaneous declipping and denoising. |
| title | A convexity preserving nonconvex regularization for inverse problems under non-Gaussian noise |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.13287 |