BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

A. Goujon, S. Neumayer, M. Unser

SIAM Journal on Imaging Sciences, vol. 17, no. 1, pp. 91–115, 2024.

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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AUTHOR="Goujon, A. and Neumayer, S. and Unser, M.",
TITLE="Learning Weakly Convex Regularizers for Convergent
	Image-Reconstruction Algorithms",
JOURNAL="{SIAM} Journal on Imaging Sciences",
YEAR="2024",
volume="17",
number="1",
pages="91--115",
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