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

A Neural-Network-Based Convex Regularizer for Inverse Problems

A. Goujon, S. Neumayer, P. Bohra, S. Ducotterd, M. Unser

IEEE Transactions on Computational Imaging, vol. 9, pp. 781–795, 2023.

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in quality. Unfortunately, these new methods often lack reliability and explainability, and there is a growing interest to address these shortcomings while retaining the boost in performance. In this work, we tackle this issue by revisiting regularizers that are the sum of convex-ridge functions. The gradient of such regularizers is parameterized by a neural network that has a single hidden layer with increasing and learnable activation functions. This neural network is trained within a few minutes as a multistep Gaussian denoiser. The numerical experiments for denoising, CT, and MRI reconstruction show improvements over methods that offer similar reliability guarantees. 

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AUTHOR="Goujon, A. and Neumayer, S. and Bohra, P. and Ducotterd, S. and
	Unser, M.",
TITLE="A Neural-Network-Based Convex Regularizer for Inverse Problems",
JOURNAL="{IEEE} Transactions on Computational Imaging",
YEAR="2023",
volume="9",
number="",
pages="781--795",
month="",
note="")

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