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.

翻译：基于深度学习的方法在解决图像重建问题中的出现，显著提升了重建质量。然而，这些新方法往往缺乏可靠性和可解释性，人们越来越关注在保持性能提升的同时解决这些不足。在本工作中，我们通过重新审视凸脊函数之和形式的正则化器来应对这一问题。此类正则化器的梯度由一个单隐藏层神经网络参数化，其激活函数是递增且可学习的。该神经网络在几分钟内作为多步高斯去噪器进行训练。去噪、CT及MRI重建的数值实验表明，该方法相较于提供类似可靠性保证的方法具有改进效果。