Learning Regularization Parameters of Inverse Problems via Deep Neural Networks

TL;DR

This paper introduces a deep neural network-based method to efficiently learn and predict regularization parameters for inverse problems, improving adaptability and potentially accuracy over traditional methods.

Contribution

The paper presents a supervised learning approach using DNNs to directly predict regularization parameters, enhancing generalizability and computational efficiency compared to existing techniques.

Findings

DNNs can predict regularization parameters more efficiently.

The approach offers better adaptability to new data.

Numerical results show promising accuracy improvements.

Abstract

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the mapping from observation data to regularization parameters. Once the network is trained, regularization parameters for newly obtained data can be computed by efficient forward propagation of the DNN. We show that a wide variety of regularization functionals, forward models, and noise models may be considered. The network-obtained regularization parameters can be computed more efficiently and may even lead to more accurate solutions compared to existing regularization parameter selection methods. We emphasize that the key advantage of using DNNs for learning regularization parameters, compared to previous works on learning via optimal experimental design or empirical Bayes risk minimization, is greater generalizability. That is, rather than computing one set of parameters that is optimal with respect to one particular design objective, DNN-computed regularization parameters are tailored to the specific features or properties of the newly observed data. Thus, our approach may better handle cases where the observation is not a close representation of the training set. Furthermore, we avoid the need for expensive and challenging bilevel optimization methods as utilized in other existing training approaches. Numerical results demonstrate the potential of using DNNs to learn regularization parameters.