Deep Learning and Inverse Problems

TL;DR

This paper reviews how deep learning techniques, especially neural networks, are applied to solve inverse problems in various fields, emphasizing methods that incorporate known physics constraints and data-driven approaches.

Contribution

It provides an overview of neural network-based methods tailored for inverse problems, highlighting the integration of physics constraints and data-driven models.

Findings

Deep learning models can effectively address ill-posed inverse problems.

Incorporating physics constraints improves solution accuracy.

Data-driven deep learning approaches offer flexible solutions.

Abstract

Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine interface, etc. In computer vision, image and video processing, these methods are mainly based on Neural Networks (NN) and in particular Convolutional NN (CNN), and more generally Deep NN. Inverse problems arise anywhere we have indirect measurement. As, in general, those inverse problems are ill-posed, to obtain satisfactory solutions for them needs prior information. Different regularization methods have been proposed, where the problem becomes the optimization of a criterion with a likelihood term and a regularization term. The main difficulty, however, in great dimensional real applications, remains the computational cost. Using NN, and in particular Deep Learning (DL) surrogate models and approximate computation, can become very helpful. In this work, we focus on NN and DL particularly adapted for inverse problems. We consider two cases: First the case where the forward operator is known and used as physics constraint, the second more general data driven DL methods.