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，目前学术界正日益关注如何在保持性能提升的同时弥补这些不足。本研究通过重新审视凸脊函数之和形式的正则化方法来解决该问题。此类正则化器的梯度由一个具有单隐藏层且激活函数递增可学习的神经网络进行参数化。该网络可在数分钟内被训练为多步高斯去噪器。在去噪、CT及MRI重建领域的数值实验表明，本方法较之具有类似可靠性保证的现有方法性能更优。