A Relaxed Gradient Step Denoiser for Splitting Methods in Poisson Inverse Problems

What the math gives to ML

The paper's transferable asset is a learned denoiser constrained to be a gradient step on a convex potential, giving an explicit route to firm nonexpansiveness rather than relying only on empirical denoising quality. This structure can be used as a stable neural operator inside plug-and-play reconstruction, recurrent refinement networks, or proximal-like layers, especially when iterates may leave the training distribution. The most practical adaptation is to parameterize an input-convex potential, enforce or estimate a global gradient-Lipschitz bound, and choose the denoising relaxation from that bound; the Poisson fidelity gradient provides a useful stress test but is not required for the architectural transfer.