EPFL | Biomedical Imaging Group

Deep-Spline Neural Networks for Stable Image Reconstruction

M. Unser

First Workshop of the SFB MR-DYNAMO (FWF'26), Graz, Republic of Austria, May 20-22, 2026.

The two dominant CNN-based paradigms for consistent biomedical image reconstruction are: (i) approaches based on trainable regularizers; and (ii) proximal-gradient-type architectures, such as plug-and-play (PnP) methods, that rely on a learned denoiser. A major challenge in both settings is the control of stability and convergence, which typically requires restrictive conditions such as convexity of the regularizer or nonexpansiveness of the denoiser. While effective from a theoretical standpoint, these constraints may reduce the representational power of the resulting models.

In this work, we propose a framework that increases model flexibility by learning the neuronal activation functions jointly with the network parameters, while maintaining explicit control over their slopes. The activations are parameterized as adaptive linear splines obtained through a second-order total-variation regularization principle. This formulation leads to parsimonious and trainable spline-based neural architectures that can be integrated within stable reconstruction schemes. We demonstrate the practicality of the proposed approach on denoising and biomedical image-reconstruction tasks, where it achieves competitive and robust performance.

Slides of the Presentation

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