EPFL | Biomedical Imaging Group | Sparsifying Regularisers

Learning Sparsifying Regularisers

S. Neumayer

Proceedings of the Eleventh Conference on Applied Inverse Problems (AIP'23), Göttingen, Federal Republic of Germany, September 4-8, 2023, pp. 175.

Solving inverse problems is possible, for example, by using variational models. First, we discuss a convex regularizer based on a one-hidden-layer neural network with (almost) free-form activation functions. Our numerical experiments have shown that this simple architecture already achieves state-of-the-art performance in the convex regime. This is very different from the non-convex case, where more complex models usually result in better performance. Inspired by this observation, we discuss an extension of our approach within the convex non-convex framework. Here, the regularizer can be non-convex, but the overall objective has to remain convex. This maintains the nice optimization properties while allowing to significantly boost the performance. Our numerical results show that this convex-energy-based approach is indeed able to outperform the popular BM3D denoiser on the BSD68 test set for various noise scales.

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