# Provably Convergent Plug & Play Linearized ADMM, applied to Deblurring Spatially Varying Kernels

arXiv: https://arxiv.org/abs/2210.10605 · HTML: https://mlsanity.com/paper/2210.10605/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 19 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [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)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [Provable Convergence of Plug-and-Play Priors with MMSE denoisers](https://mlsanity.com/paper/2005.07685/) (2020)
- [On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent](https://mlsanity.com/paper/2201.06133/) (2022)
- [Linearized ADMM for Non-convex Non-smooth Optimization with Convergence Analysis](https://mlsanity.com/paper/1705.02502/) (2017)
- [Plug-and-play ISTA converges with kernel denoisers](https://mlsanity.com/paper/2004.03145/) (2020)
- [Fast Single Image Super-Resolution](https://mlsanity.com/paper/1510.00143/) (2015)
- [Non-uniform Blur Kernel Estimation via Adaptive Basis Decomposition](https://mlsanity.com/paper/2102.01026/) (2021)
- [Deep Model-Based Super-Resolution with Non-uniform Blur](https://mlsanity.com/paper/2204.10109/) (2022)
- [Image restoration using sparse approximations of spatially varying blur operators in the wavelet domain](https://mlsanity.com/paper/1302.6105/) (2013)

## Built on by (most cited first, 2 of 2)

- [Learning pseudo-contractive denoisers for inverse problems](https://mlsanity.com/paper/2402.05637/) (2024)
- [Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problems](https://mlsanity.com/paper/2505.08909/) (2025)

## Abstract (arXiv)

Plug & Play methods combine proximal algorithms with denoiser priors to solve inverse problems. These methods rely on the computability of the proximal operator of the data fidelity term. In this paper, we propose a Plug & Play framework based on linearized ADMM that allows us to bypass the computation of intractable proximal operators. We demonstrate the convergence of the algorithm and provide results on restoration tasks such as super-resolution and deblurring with non-uniform blur.