Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

• URL: http://arxiv.org/abs/2308.10542v2
• Date: Wed, 20 Dec 2023 11:17:24 GMT
• Title: Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms
• Authors: Alexis Goujon, Sebastian Neumayer, Michael Unser
• Abstract summary: We propose to learn non-processing regularizers with a bound on their weak energy. We show that they mimic convexs-regularity-promoting regularizers. We also show that the learned regularizer can be deployed to solve inverse problems with schemes provably converge.
• Score: 16.78532039510369
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000) and offer a signal-processing interpretation as they mimic handcrafted sparsity-promoting regularizers. Through numerical experiments, we show that such denoisers outperform convex-regularization methods as well as the popular BM3D denoiser. Additionally, the learned regularizer can be deployed to solve inverse problems with iterative schemes that provably converge. For both CT and MRI reconstruction, the regularizer generalizes well and offers an excellent tradeoff between performance, number of parameters, guarantees, and interpretability when compared to other data-driven approaches.

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