# Regularization of Inverse Problems by Neural Networks

arXiv: https://arxiv.org/abs/2006.03972 · HTML: https://mlsanity.com/paper/2006.03972/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2020.

## Built on by (most cited first, 6 of 6)

- [Noisier2Inverse: Self-Supervised Learning for Image Reconstruction with Correlated Noise](https://mlsanity.com/paper/2503.19468/) (2025)
- [Multi-Parameter Molecular MRI Quantification using Physics-Informed Self-Supervised Learning](https://mlsanity.com/paper/2411.06447/) (2024)
- [Position: Stop Making Unscientific AGI Performance Claims](https://mlsanity.com/paper/2402.03962/) (2024)
- [Uncertainty-Aware Null Space Networks for Data-Consistent Image Reconstruction](https://mlsanity.com/paper/2304.06955/) (2023)
- [Inverting Non-Injective Functions with Twin Neural Network Regression](https://mlsanity.com/paper/2601.05378/) (2026)
- [Self-Supervised Angular Deblurring in Photoacoustic Reconstruction via Noisier2Inverse](https://mlsanity.com/paper/2604.15681/) (2026)

## Abstract (arXiv)

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their solutions. Therefore, any reasonable solution method requires the use of regularization tools that select specific solutions and at the same time stabilize the inversion process. Recently, data-driven methods using deep learning techniques and neural networks demonstrated to significantly outperform classical solution methods for inverse problems. In this chapter, we give an overview of inverse problems and demonstrate the necessity of regularization concepts for their solution. We show that neural networks can be used for the data-driven solution of inverse problems and review existing deep learning methods for inverse problems. In particular, we view these deep learning methods from the perspective of regularization theory, the mathematical foundation of stable solution methods for inverse problems. This chapter is more than just a review as many of the presented theoretical results extend existing ones.