mlsanityData to 14 Oct 2026

DRIP: Deep Regularizers for Inverse Problems

arXiv 2304.00015 ↗First posted 30 Mar 2023cs.LG cs.CEcited by 7

Not on the map. Why?

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.

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

20 of 46 references.

References · 20

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  4. 2021Convex optimizationcited by 2,515
  5. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 433
  6. 2017MoDL: Model Based Deep Learning Architecture for Inverse Problemscited by 387
  7. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 291
  8. 2015Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restorationcited by 195
  9. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  10. 2017Solving ill-posed inverse problems using iterative deep neural networkscited by 145
  11. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  12. 2018Neural Proximal Gradient Descent for Compressive Imagingcited by 46
8 more
  1. 2020The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problemscited by 40
  2. 2021Learning Regularization Parameters of Inverse Problems via Deep Neural Networkscited by 19
  3. 2020Deep Learning Methods for Solving Linear Inverse Problems: Research Directions and Paradigmscited by 16
  4. 2021Mimetic Neural Networks: A unified framework for Protein Design and Foldingcited by 7
  5. 2021Unsupervised Knowledge-Transfer for Learned Image Reconstructioncited by 4
  6. 2020Data-consistent neural networks for solving nonlinear inverse problemscited by 3
  7. 2016A multilevel framework for sparse optimization with application to inverse covariance estimation and logistic regressioncited by 2
  8. 2022Estimating a potential without the agony of the partition functioncited by 2

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 4; 2025: 2.

7 papers.

  1. 2024Paired Autoencoders for Likelihood-free Estimation in Inverse Problemscited by 6
  2. 2024An Over Complete Deep Learning Method for Inverse Problemscited by 3
  3. 2024Learning Regularization for Graph Inverse Problemscited by 3
  4. 2023A Test-Time Learning Approach to Reparameterize the Geophysical Inverse Problem with a Convolutional Neural Networkcited by 2
  5. 2024DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problemscited by 2
  6. 2025Graph Neural Regularizers for PDE Inverse Problemscited by 1
  7. 2025Deep regularization networks for inverse problems with noisy operatorscited by 0