# Solving Inverse Problems with Model Mismatch using Untrained Neural Networks within Model-based Architectures

arXiv: https://arxiv.org/abs/2403.04847 · HTML: https://mlsanity.com/paper/2403.04847/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 57 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 21 of 21)

- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurring](https://mlsanity.com/paper/2103.09962/) (2021)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Model Adaptation for Inverse Problems in Imaging](https://mlsanity.com/paper/2012.00139/) (2020)
- [Learning Provably Robust Estimators for Inverse Problems via Jittering](https://mlsanity.com/paper/2307.12822/) (2023)
- [Approximate k-space models and Deep Learning for fast photoacoustic reconstruction](https://mlsanity.com/paper/1807.03191/) (2018)
- [Loop Unrolled Shallow Equilibrium Regularizer (LUSER) -- A Memory-Efficient Inverse Problem Solver](https://mlsanity.com/paper/2210.04987/) (2022)
- [Robustness of Deep Equilibrium Architectures to Changes in the Measurement Model](https://mlsanity.com/paper/2211.00531/) (2022)
- [Model reduction in acoustic inversion by artificial neural network](https://mlsanity.com/paper/2105.02225/) (2021)

## Built on by (most cited first, 3 of 3)

- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)
- [SGD Jittering: A Training Strategy for Robust and Accurate Model-Based Architectures](https://mlsanity.com/paper/2410.14667/) (2024)
- [Neural Fields for NV-Center Inverse Sensing](https://mlsanity.com/paper/2605.13988/) (2026)

## Abstract (arXiv)

Model-based deep learning methods such as loop unrolling (LU) and deep equilibrium model(DEQ) extensions offer outstanding performance in solving inverse problems (IP). These methods unroll the optimization iterations into a sequence of neural networks that in effect learn a regularization function from data. While these architectures are currently state-of-the-art in numerous applications, their success heavily relies on the accuracy of the forward model. This assumption can be limiting in many physical applications due to model simplifications or uncertainties in the apparatus. To address forward model mismatch, we introduce an untrained forward model residual block within the model-based architecture to match the data consistency in the measurement domain for each instance. We propose two variants in well-known model-based architectures (LU and DEQ) and prove convergence under mild conditions. Our approach offers a unified solution that is less parameter-sensitive, requires no additional data, and enables simultaneous fitting of the forward model and reconstruction in a single pass, benefiting both linear and nonlinear inverse problems. The experiments show significant quality improvement in removing artifacts and preserving details across three distinct applications, encompassing both linear and nonlinear inverse problems. Moreover, we highlight reconstruction effectiveness in intermediate steps and showcase robustness to random initialization of the residual block and a higher number of iterations during evaluation. Code is available at texttthttps://github.com/InvProbs/A-adaptive-model-based-methods.