Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problems
Journal:
arXiv
Published Date:
May 13, 2025
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.
