# Overcoming Distribution Shifts in Plug-and-Play Methods with Test-Time Training

arXiv: https://arxiv.org/abs/2403.10374 · HTML: https://mlsanity.com/paper/2403.10374/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 15 Mar 2024.

## Builds on (most cited first, 11 of 11)

- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [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)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation](https://mlsanity.com/paper/1512.07331/) (2015)
- [Test-Time Training Can Close the Natural Distribution Shift Performance Gap in Deep Learning Based Compressed Sensing](https://mlsanity.com/paper/2204.07204/) (2022)
- [Online Deep Equilibrium Learning for Regularization by Denoising](https://mlsanity.com/paper/2205.13051/) (2022)
- [Deep Model-Based Architectures for Inverse Problems under Mismatched Priors](https://mlsanity.com/paper/2207.13200/) (2022)

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

- [Fast MRI for All: Bridging Access Gaps by Training without Raw Data](https://mlsanity.com/paper/2411.13022/) (2024)
- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)
- [Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2607.14894/) (2026)

## Abstract (arXiv)

Plug-and-Play Priors (PnP) is a well-known class of methods for solving inverse problems in computational imaging. PnP methods combine physical forward models with learned prior models specified as image denoisers. A common issue with the learned models is that of a performance drop when there is a distribution shift between the training and testing data. Test-time training (TTT) was recently proposed as a general strategy for improving the performance of learned models when training and testing data come from different distributions. In this paper, we propose PnP-TTT as a new method for overcoming distribution shifts in PnP. PnP-TTT uses deep equilibrium learning (DEQ) for optimizing a self-supervised loss at the fixed points of PnP iterations. PnP-TTT can be directly applied on a single test sample to improve the generalization of PnP. We show through simulations that given a sufficient number of measurements, PnP-TTT enables the use of image priors trained on natural images for image reconstruction in magnetic resonance imaging (MRI).