# Instabilities in Plug-and-Play (PnP) algorithms from a learned denoiser

arXiv: https://arxiv.org/abs/2109.01655 · HTML: https://mlsanity.com/paper/2109.01655/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 17 Aug 2021.

## Builds on (most cited first, 8 of 8)

- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [An Online Plug-and-Play Algorithm for Regularized Image Reconstruction](https://mlsanity.com/paper/1809.04693/) (2018)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibrium](https://mlsanity.com/paper/1705.08983/) (2017)
- [Interpretation of Plug-and-Play (PnP) algorithms from a different angle](https://mlsanity.com/paper/2106.07795/) (2021)

## Built on by (most cited first, 1 of 1)

- [Regularizing Instabilities in Image Reconstruction Arising from Learned Denoisers](https://mlsanity.com/paper/2108.13551/) (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 are the penalized Variational approaches. In recent years, the classical regularization approaches have been outclassed by the so-called plug-and-play (PnP) algorithms, which copy the proximal gradient minimization processes, such as ADMM or FISTA, but with any general denoiser. However, unlike the traditional proximal gradient methods, the theoretical underpinnings, convergence, and stability results have been insufficient for these PnP-algorithms. Hence, the results obtained from these algorithms, though empirically outstanding, can't always be completely trusted, as they may contain certain instabilities or (hallucinated) features arising from the denoiser, especially when using a pre-trained learned denoiser. In fact, in this paper, we show that a PnP-algorithm can induce hallucinated features, when using a pre-trained deep-learning-based (DnCNN) denoiser. We show that such instabilities are quite different than the instabilities inherent to an ill-posed problem. We also present methods to subdue these instabilities and significantly improve the recoveries. We compare the advantages and disadvantages of a learned denoiser over a classical denoiser (here, BM3D), as well as, the effectiveness of the FISTA-PnP algorithm vs. the ADMM-PnP algorithm. In addition, we also provide an algorithm to combine these two denoisers, the learned and the classical, in a weighted fashion to produce even better results. We conclude with numerical results which validate the developed theories.