# DRIP: Deep Regularizers for Inverse Problems

arXiv: https://arxiv.org/abs/2304.00015 · HTML: https://mlsanity.com/paper/2304.00015/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 30 Mar 2023.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems](https://mlsanity.com/paper/2001.01258/) (2020)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [Deep Learning Methods for Solving Linear Inverse Problems: Research Directions and Paradigms](https://mlsanity.com/paper/2007.13290/) (2020)
- [Mimetic Neural Networks: A unified framework for Protein Design and Folding](https://mlsanity.com/paper/2102.03881/) (2021)
- [Unsupervised Knowledge-Transfer for Learned Image Reconstruction](https://mlsanity.com/paper/2107.02572/) (2021)
- [Data-consistent neural networks for solving nonlinear inverse problems](https://mlsanity.com/paper/2003.11253/) (2020)
- [A multilevel framework for sparse optimization with application to inverse covariance estimation and logistic regression](https://mlsanity.com/paper/1607.00315/) (2016)
- [Estimating a potential without the agony of the partition function](https://mlsanity.com/paper/2208.09433/) (2022)

## Built on by (most cited first, 7 of 7)

- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [An Over Complete Deep Learning Method for Inverse Problems](https://mlsanity.com/paper/2402.04653/) (2024)
- [Learning Regularization for Graph Inverse Problems](https://mlsanity.com/paper/2408.10436/) (2024)
- [A Test-Time Learning Approach to Reparameterize the Geophysical Inverse Problem with a Convolutional Neural Network](https://mlsanity.com/paper/2312.04752/) (2023)
- [DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems](https://mlsanity.com/paper/2412.04766/) (2024)
- [Graph Neural Regularizers for PDE Inverse Problems](https://mlsanity.com/paper/2510.21012/) (2025)
- [Deep regularization networks for inverse problems with noisy operators](https://mlsanity.com/paper/2506.07008/) (2025)

## Abstract (arXiv)

In this paper we consider inverse problems that are mathematically ill-posed. That is, given some (noisy) data, there is more than one solution that approximately fits the data. In recent years, deep neural techniques that find the most appropriate solution, in the sense that it contains a-priori information, were developed. However, they suffer from several shortcomings. First, most techniques cannot guarantee that the solution fits the data at inference. Second, while the derivation of the techniques is inspired by the existence of a valid scalar regularization function, such techniques do not in practice rely on such a function, and therefore veer away from classical variational techniques. In this work we introduce a new family of neural regularizers for the solution of inverse problems. These regularizers are based on a variational formulation and are guaranteed to fit the data. We demonstrate their use on a number of highly ill-posed problems, from image deblurring to limited angle tomography.