# A Viscosity Semigroup Framework for Stable Image Reconstruction

arXiv: https://arxiv.org/abs/2606.20620 · HTML: https://mlsanity.com/paper/2606.20620/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 14 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 1 of 1)

- [High Confidence Level Inference is Almost Free using Parallel Stochastic Optimization](https://mlsanity.com/paper/2401.09346/) (2024)

## Abstract (arXiv)

Starting from the axiomatic formulation of scale-space theory, we develop a viscosity-solution framework for multiscale image representations arising from degenerate elliptic-parabolic partial differential equations. Rather than introducing a new semigroup theory, we work within the standard viscosity-solution setting, using comparison principles to obtain well-posedness, uniqueness, and contraction in the supremum norm. This perspective is used to motivate a hybrid reconstruction operator in which a learned inverse map is followed by a nonlinear diffusion evolution. At the continuous level, the diffusion operator satisfies non-expansiveness, which provides stability for the reconstruction process; this framework is then evaluated on a CT-based mesothelioma classification task, where it attains an AUC of 0.875 with negligible variation across epochs, while the baseline model acquires AUC values from 0.49 to 0.80 without a clear convergence pattern. These observations are consistent with the stabilizing role suggested by the discussed viscosity theory.