A convexity preserving nonconvex regularization for inverse problems under non-Gaussian noise
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.
Cite
@article{arxiv.2503.13287,
title = {A convexity preserving nonconvex regularization for inverse problems under non-Gaussian noise},
author = {Wataru Yata and Keita Kume and Isao Yamada},
journal= {arXiv preprint arXiv:2503.13287},
year = {2025}
}