# Survey of Deep Learning Methods for Inverse Problems

arXiv: https://arxiv.org/abs/2111.04731 · HTML: https://mlsanity.com/paper/2111.04731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 66 references that are in the map.
- First posted on arXiv 7 Nov 2021.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [An Analysis of Deep Neural Network Models for Practical Applications](https://mlsanity.com/paper/1605.07678/) (2016)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [Learning to Deblur](https://mlsanity.com/paper/1406.7444/) (2014)
- [A Comprehensive Analysis of Deep Regression](https://mlsanity.com/paper/1803.08450/) (2018)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [Long Short-Term Memory Kalman Filters:Recurrent Neural Estimators for Pose Regularization](https://mlsanity.com/paper/1708.01885/) (2017)
- [Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problems](https://mlsanity.com/paper/1904.05417/) (2019)
- [Regularization by architecture: A deep prior approach for inverse problems](https://mlsanity.com/paper/1812.03889/) (2018)
- [Learning to Invert: Signal Recovery via Deep Convolutional Networks](https://mlsanity.com/paper/1701.03891/) (2017)
- [Deep Learning for Photoacoustic Tomography from Sparse Data](https://mlsanity.com/paper/1704.04587/) (2017)
- [Self-Supervised Physics-Based Deep Learning MRI Reconstruction Without Fully-Sampled Data](https://mlsanity.com/paper/1910.09116/) (2019)
- [An Unsupervised Approach to Solving Inverse Problems using Generative Adversarial Networks](https://mlsanity.com/paper/1805.07281/) (2018)
- [Online Visual Multi-Object Tracking via Labeled Random Finite Set Filtering](https://mlsanity.com/paper/1611.06011/) (2016)
- [Deep Learning-Guided Image Reconstruction from Incomplete Data](https://mlsanity.com/paper/1709.00584/) (2017)
- [The structure of optimal parameters for image restoration problems](https://mlsanity.com/paper/1505.01953/) (2015)
- [InverseNet: Solving Inverse Problems with Splitting Networks](https://mlsanity.com/paper/1712.00202/) (2017)
- [Biomedical Image Reconstruction: From the Foundations to Deep Neural Networks](https://mlsanity.com/paper/1901.03565/) (2019)

## Built on by (most cited first, 1 of 1)

- [Learning Control by Iterative Inversion](https://mlsanity.com/paper/2211.01724/) (2022)

## Abstract (arXiv)

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep Regularizer. We choose a sample of each inverse problem type, so as to compare the robustness of the three categories, and report a statistical analysis of their differences. We perform extensive experiments on the classic problem of linear regression and three well-known inverse problems in computer vision, namely image denoising, 3D human face inverse rendering, and object tracking, selected as representative prototypes for each class of inverse problems. The overall results and the statistical analyses show that the solution categories have a robustness behaviour dependent on the type of inverse problem domain, and specifically dependent on whether or not the problem includes measurement outliers. Based on our experimental results, we conclude by proposing the most robust solution category for each inverse problem class.