  The emergence of deep-learning-based methods to solve image-reconstruction
problems has enabled a significant increase in reconstruction 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.
