Single-Shot Plug-and-Play Methods for Inverse Problems


Yanqi Cheng
Lipei Zhang*
Zhenda Shen*
Shujun Wang
Lequan Yu
Raymond H. Chan
Carola-Bibiane Schönlieb
Angelica I. Aviles-Rivero

affiliations


The visualisation of our proposed framework.
This is a website made for Single-Shot Plug-and-Play Methods for Inverse Problems.

Abstract

The utilisation of Plug-and-Play (PnP) priors in inverse problems has become increasingly prominent in recent years. This preference is based on the mathematical equivalence between the general proximal operator and the regularised denoiser, facilitating the adaptation of various off-the-shelf denoiser priors to a wide range of inverse problems. However, existing PnP models predominantly rely on pre-trained denoisers using large datasets. In this work, we introduce Single-Shot PnP methods (SS-PnP), shifting the focus to solving inverse problems with minimal data. First, we integrate Single-Shot proximal denoisers into iterative methods, enabling training with single instances. Second, we propose implicit neural priors based on a novel function that preserves relevant frequencies to capture fine details while avoiding the issue of vanishing gradients. We demonstrate, through extensive numerical and visual experiments, that our method leads to better approximations.

The visualisation of Super-resolution (SR) task. Super-resolution (SR)
The visualisation of Image Deconvolution task. Image Deconvolution
The visualisation of Joint Demosaicing and Deconvolution task. Joint Demosaicing and Deconvolution

Paper and Supplementary Material


Yanqi Cheng, Lipei Zhang*, Zhenda Shen*, Shujun Wang, Lequan Yu, Raymond H. Chan, Carola-Bibiane Schönlieb, Angelica I Aviles-Rivero.
Single-Shot Plug-and-Play Methods for Inverse Problems
Transactions on Machine Learning Research

[Paper]   [Bibtex]


Acknowledgements

This project was supported with funding from the Cambridge Centre for Data-Driven Discovery and Accelerate Programme for Scientific Discovery, made possible by a donation from Schmidt Futures. ZS acknowledges support from the Department of Mathematics, College of Science, CityU, and HKASR reaching out award. RHC acknowledges support from HKRGC GRF grants CityU1101120 and CityU11309922 and CRF grant C1013-21GF. AIAR acknowledges support from CMIH (EP/T017961/1) and CCIMI, University of Cambridge. This work was supported in part by Oracle Cloud credits and related resources provided by Oracle for Research. Also, EPSRC Digital Core Capability. CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC advanced career fellowship EP/V029428/1, EPSRC grants EP/S026045/1 and EP/T003553/1, EP/N014588/1, EP/T017961/1, the Wellcome Innovator Awards 215733/Z/19/Z and 221633/Z/20/Z, the European Union Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute.