# Deep Learning and Inverse Problems

arXiv: https://arxiv.org/abs/2309.00802 · HTML: https://mlsanity.com/paper/2309.00802/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 2 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification](https://mlsanity.com/paper/1812.09444/) (2018)
- [Learning Deep Gradient Descent Optimization for Image Deconvolution](https://mlsanity.com/paper/1804.03368/) (2018)
- [Regularized deep learning with nonconvex penalties](https://mlsanity.com/paper/1909.05142/) (2019)

## Abstract (arXiv)

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.