Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problems

• URL: http://arxiv.org/abs/2505.08909v1
• Date: Tue, 13 May 2025 19:00:55 GMT
• Title: Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problems
• Authors: Deliang Wei, Peng Chen, Haobo Xu, Jiale Yao, Fang Li, Tieyong Zeng,
• Abstract summary: We propose a cocoercive conservative (CoCo) denoiser, which may be (residual) expansive, leading to improved denoising.<n>By leveraging the generalized Helmholtz decomposition, we introduce a novel training strategy that combines Hamiltonian regularization to promote conservativeness.
• Score: 17.861078961765966
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Plug-and-play (PnP) methods with deep denoisers have shown impressive results in imaging problems. They typically require strong convexity or smoothness of the fidelity term and a (residual) non-expansive denoiser for convergence. These assumptions, however, are violated in Poisson inverse problems, and non-expansiveness can hinder denoising performance. To address these challenges, we propose a cocoercive conservative (CoCo) denoiser, which may be (residual) expansive, leading to improved denoising. By leveraging the generalized Helmholtz decomposition, we introduce a novel training strategy that combines Hamiltonian regularization to promote conservativeness and spectral regularization to ensure cocoerciveness. We prove that CoCo denoiser is a proximal operator of a weakly convex function, enabling a restoration model with an implicit weakly convex prior. The global convergence of PnP methods to a stationary point of this restoration model is established. Extensive experimental results demonstrate that our approach outperforms closely related methods in both visual quality and quantitative metrics.

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