# Data-Consistent Learning of Inverse Problems

arXiv: https://arxiv.org/abs/2601.12831 · HTML: https://mlsanity.com/paper/2601.12831/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [On hallucinations in tomographic image reconstruction](https://mlsanity.com/paper/2012.00646/) (2020)
- [Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography](https://mlsanity.com/paper/1811.04602/) (2018)
- [Deep Decomposition Learning for Inverse Imaging Problems](https://mlsanity.com/paper/1911.11028/) (2019)
- [Deep Residual Learning for Compressed Sensing CT Reconstruction via Persistent Homology Analysis](https://mlsanity.com/paper/1611.06391/) (2016)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [Data-consistent neural networks for solving nonlinear inverse problems](https://mlsanity.com/paper/2003.11253/) (2020)
- [A Projectional Ansatz to Reconstruction](https://mlsanity.com/paper/1907.04675/) (2019)
- [Data Consistent CT Reconstruction from Insufficient Data with Learned Prior Images](https://mlsanity.com/paper/2005.10034/) (2020)
- [Neural Networks-based Regularization for Large-Scale Medical Image Reconstruction](https://mlsanity.com/paper/1912.09395/) (2019)
- [Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches](https://mlsanity.com/paper/2506.17465/) (2025)

## Abstract (arXiv)

Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced flexibility or visual quality. Learned reconstruction methods, such as convolutional neural networks, can produce visually compelling results, yet they typically lack rigorous theoretical guarantees. DC (DC) networks address this gap by enforcing the measurement model within the network architecture. In particular, null-space networks combined with a classical regularization method as an initial reconstruction define a convergent regularization method. This approach preserves the theoretical reliability of classical schemes while leveraging the expressive power of data-driven learning, yielding reconstructions that are both accurate and visually appealing.