A convexity preserving nonconvex regularization for inverse problems under non-Gaussian noise
Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Yata, Wataru, Kume, Keita, Yamada, Isao
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979332863
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