# Learned Regularization for Inverse Problems: Insights from a Spectral Model

arXiv: https://arxiv.org/abs/2312.09845 · HTML: https://mlsanity.com/paper/2312.09845/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 15 Dec 2023.

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

- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Learned reconstruction methods with convergence guarantees](https://mlsanity.com/paper/2206.05431/) (2022)
- [Learning the optimal Tikhonov regularizer for inverse problems](https://mlsanity.com/paper/2106.06513/) (2021)
- [Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography](https://mlsanity.com/paper/2006.01620/) (2020)
- [Learning convex regularizers satisfying the variational source condition for inverse problems](https://mlsanity.com/paper/2110.12520/) (2021)
- [Convergent Data-driven Regularizations for CT Reconstruction](https://mlsanity.com/paper/2212.07786/) (2022)

## Built on by (most cited first, 2 of 2)

- [Structure is information: structural identifiability mappings for machine learning with partially observed dynamical systems](https://mlsanity.com/paper/2502.04131/) (2025)
- [Bayesian Model Parameter Learning in Linear Inverse Problems: Application in EEG Focal Source Imaging](https://mlsanity.com/paper/2501.13109/) (2025)

## Abstract (arXiv)

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization methods and their convergence in terms of the underlying data distributions, which paves the way for future theoretical studies. Based on a simple spectral learning model previously introduced for supervised learning, we investigate some key properties of different learning paradigms for inverse problems, which can be formulated independently of specific architectures. In particular we investigate the regularization properties, bias, and critical dependence on training data distributions. Moreover, our framework allows to highlight and compare the specific behavior of the different paradigms in the infinite-dimensional limit.