# Regularizing Instabilities in Image Reconstruction Arising from Learned Denoisers

arXiv: https://arxiv.org/abs/2108.13551 · HTML: https://mlsanity.com/paper/2108.13551/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 21 Aug 2021.

## Builds on (most cited first, 12 of 12)

- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [CNN-Based Projected Gradient Descent for Consistent Image Reconstruction](https://mlsanity.com/paper/1709.01809/) (2017)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [Multi-Scale Learned Iterative Reconstruction](https://mlsanity.com/paper/1908.00936/) (2019)
- [Interpretation of Plug-and-Play (PnP) algorithms from a different angle](https://mlsanity.com/paper/2106.07795/) (2021)
- [Instabilities in Plug-and-Play (PnP) algorithms from a learned denoiser](https://mlsanity.com/paper/2109.01655/) (2021)

## Abstract (arXiv)

It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, popular regularization methods have been the penalized Variational approaches. In recent years, the classical regularized-reconstruction approaches have been outclassed by the (deep-learning-based) learned reconstruction algorithms. However, unlike the traditional regularization methods, the theoretical underpinnings, such as stability and regularization, have been insufficient for such learned reconstruction algorithms. Hence, the results obtained from such algorithms, though empirically outstanding, can't always be completely trusted, as they may contain certain instabilities or (hallucinated) features arising from the learned process. In fact, it has been shown that such learning algorithms are very susceptible to small (adversarial) noises in the data and can lead to severe instabilities in the recovered solution, which can be quite different than the inherent instabilities of the ill-posed (inverse) problem. Whereas, the classical regularization methods can handle such (adversarial) noises very well and can produce stable recovery. Here, we try to present certain regularization methods to stabilize such (unstable) learned reconstruction methods and recover a regularized solution, even in the presence of adversarial noises. For this, we need to extend the classical notion of regularization and incorporate it in the learned reconstruction algorithms. We also present some regularization techniques to regularize two of the most popular learning reconstruction algorithms, the Learned Post-Processing Reconstruction and the Learned Unrolling Reconstruction.