A Viscosity Semigroup Framework for Stable Image Reconstruction

• URL: http://arxiv.org/abs/2606.20620v1
• Date: Tue, 26 May 2026 03:41:45 GMT
• Title: A Viscosity Semigroup Framework for Stable Image Reconstruction
• Abstract summary: We develop a viscosity-solution framework for multiscale image representations arising from degenerate elliptic-parabolic partial differential equations.<n>This framework is evaluated on a CT-based mesothelioma classification task, where it attains an AUC of 0.875 with negligible variation across epochs.<n>These observations are consistent with the stabilizing role suggested by the discussed viscosity theory.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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.

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