A Neural-Network-Based Convex Regularizer for Inverse Problems
This addresses reliability issues in medical imaging reconstruction, though it is incremental as it builds on existing convex regularizer frameworks.
The paper tackles the lack of reliability and explainability in deep-learning-based image reconstruction by proposing a convex regularizer parameterized by a neural network, showing improvements in denoising, CT, and MRI reconstruction over methods with similar guarantees.
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.