# Deep Learning and Bayesian inference for Inverse Problems

arXiv: https://arxiv.org/abs/2308.15492 · HTML: https://mlsanity.com/paper/2308.15492/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 28 Aug 2023.

## Builds on (most cited first, 6 of 6)

- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [Learning Deep Gradient Descent Optimization for Image Deconvolution](https://mlsanity.com/paper/1804.03368/) (2018)
- [Linear Response Methods for Accurate Covariance Estimates from Mean Field Variational Bayes](https://mlsanity.com/paper/1506.04088/) (2015)
- [The Practicality of Stochastic Optimization in Imaging Inverse Problems](https://mlsanity.com/paper/1910.10100/) (2019)

## Abstract (arXiv)

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based methods have been proposed. As these methods need a great number of forward and backward computations, they become costly in computation, in particular, when the forward or generative models are complex and the evaluation of the likelihood becomes very costly. Using Deep Neural Network surrogate models and approximate computation can become very helpful. However, accounting for the uncertainties, we need first understand the Bayesian Deep Learning and then, we can see how we can use them for inverse problems. In this work, we focus on NN, DL and more specifically the Bayesian DL particularly adapted for inverse problems. We first give details of Bayesian DL approximate computations with exponential families, then we will see how we can use them 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. keyword: Neural Network, Variational Bayesian inference, Bayesian Deep Learning (DL), Inverse problems, Physics based DL.