Viscosity Semigroup Framework Boosts CT Image Stability to 0.875 AUC

Arina Oberoi has published a new framework for stable image reconstruction, leveraging viscosity solutions and semigroup theory from degenerate elliptic-parabolic partial differential equations. Rather than introducing new mathematical machinery, the work operates within standard viscosity-solution settings, using comparison principles to guarantee well-posedness, uniqueness, and contraction in the supremum norm. The core innovation is a hybrid reconstruction operator: first, a learned inverse map processes raw CT data; then, a nonlinear diffusion evolution refines the output. The diffusion operator is designed to be non-expansive at the continuous level, providing theoretical stability guarantees that translate into robust empirical performance.

On a CT-based mesothelioma classification task, the framework achieved an AUC of 0.875 with negligible variation across training epochs. In contrast, the baseline model produced AUC values ranging from 0.49 to 0.80 without converging. This dramatic improvement in consistency is attributed to the stabilizing role of the viscosity theory. The work bridges classical scale-space axiomatics with modern deep learning, offering a principled way to make image reconstruction models more reliable for clinical use. The paper is available on arXiv under reference arXiv:2606.20620.