A geometry-based deep equilibrium model for image restoration under multiplicative Gamma noise

What the math gives to ML

The paper combines a positive-domain Gamma-noise fidelity with an explicit geometric regularizer involving surface area and mean curvature, then minimizes the resulting nonconvex objective by mirror descent inside a deep-equilibrium construction. The transferable asset is not merely the image-restoration application: entropy mirror geometry gives multiplicative, positivity-preserving updates, while curvature terms provide a low-parameter inductive bias that can replace a large implicit denoiser. A practical neural-network adaptation is a DEQ restoration layer whose equilibrium is computed by exponentiated mirror-descent iterations, with only a few learned geometric coefficients and step sizes. The approach is especially attractive for scientific imaging because it directly matches signal-dependent noise and offers a falsifiable parameter-count and stability advantage over an unconstrained implicit CNN prior.