# Regularization of Inverse Problems: Deep Equilibrium Models versus Bilevel Learning

arXiv: https://arxiv.org/abs/2206.13193 · HTML: https://mlsanity.com/paper/2206.13193/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2022.

## Built on by (most cited first, 4 of 4)

- [Convergent Data-driven Regularizations for CT Reconstruction](https://mlsanity.com/paper/2212.07786/) (2022)
- [Deep equilibrium models as estimators for continuous latent variables](https://mlsanity.com/paper/2211.05943/) (2022)
- [Convergence analysis of equilibrium methods for inverse problems](https://mlsanity.com/paper/2306.01421/) (2023)
- [Meta-Prior: Meta learning for Adaptive Inverse Problem Solvers](https://mlsanity.com/paper/2311.18710/) (2023)

## Abstract (arXiv)

Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert model (Roth and Black, 2009). Training the parameters of such data-driven methods can be formulated as a bilevel optimization problem. In this paper, we compare the framework of bilevel learning for the training of data-driven variational regularization models with the novel framework of deep equilibrium models (Bai, Kolter, and Koltun, 2019) that has recently been introduced in the context of inverse problems (Gilton, Ongie, and Willett, 2021). We show that computing the lower-level optimization problem within the bilevel formulation with a fixed point iteration is a special case of the deep equilibrium framework. We compare both approaches computationally, with a variety of numerical examples for the inverse problems of denoising, inpainting and deconvolution.