Goujon, AlexisNeumayer, SebastianBohra, PakshalDucotterd, StanislasUnser, Michael2023-09-192023-09-19202310.1109/TCI.2023.3306100https://infoscience.epfl.ch/handle/20.500.14299/200789The 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.text::journal::journal article::research article