Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis

Shirin Shoushtari, Jiaming Liu, Edward P. Chandler, M. Salman Asif, Ulugbek S. Kamilov
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:45154-45182, 2024.

Abstract

Plug-and-Play (PnP) priors is a widely-used family of methods for solving imaging inverse problems by integrating physical measurement models with image priors specified using image denoisers. PnP methods have been shown to achieve state-of-the-art performance when the prior is obtained using powerful deep denoisers. Despite extensive work on PnP, the topic of distribution mismatch between the training and testing data has often been overlooked in the PnP literature. This paper presents a set of new theoretical and numerical results on the topic of prior distribution mismatch and domain adaptation for the alternating direction method of multipliers (ADMM) variant of PnP. Our theoretical result provides an explicit error bound for PnP-ADMM due to the mismatch between the desired denoiser and the one used for inference. Our analysis contributes to the work in the area by considering the mismatch under nonconvex data-fidelity terms and expansive denoisers. Our first set of numerical results quantifies the impact of the prior distribution mismatch on the performance of PnP-ADMM on the problem of image super-resolution. Our second set of numerical results considers a simple and effective domain adaption strategy that closes the performance gap due to the use of mismatched denoisers. Our results suggest the relative robustness of PnP-ADMM to prior distribution mismatch, while also showing that the performance gap can be significantly reduced with only a few training samples from the desired distribution.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-shoushtari24a, title = {Prior Mismatch and Adaptation in {P}n{P}-{ADMM} with a Nonconvex Convergence Analysis}, author = {Shoushtari, Shirin and Liu, Jiaming and Chandler, Edward P. and Asif, M. Salman and Kamilov, Ulugbek S.}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {45154--45182}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/shoushtari24a/shoushtari24a.pdf}, url = {https://proceedings.mlr.press/v235/shoushtari24a.html}, abstract = {Plug-and-Play (PnP) priors is a widely-used family of methods for solving imaging inverse problems by integrating physical measurement models with image priors specified using image denoisers. PnP methods have been shown to achieve state-of-the-art performance when the prior is obtained using powerful deep denoisers. Despite extensive work on PnP, the topic of distribution mismatch between the training and testing data has often been overlooked in the PnP literature. This paper presents a set of new theoretical and numerical results on the topic of prior distribution mismatch and domain adaptation for the alternating direction method of multipliers (ADMM) variant of PnP. Our theoretical result provides an explicit error bound for PnP-ADMM due to the mismatch between the desired denoiser and the one used for inference. Our analysis contributes to the work in the area by considering the mismatch under nonconvex data-fidelity terms and expansive denoisers. Our first set of numerical results quantifies the impact of the prior distribution mismatch on the performance of PnP-ADMM on the problem of image super-resolution. Our second set of numerical results considers a simple and effective domain adaption strategy that closes the performance gap due to the use of mismatched denoisers. Our results suggest the relative robustness of PnP-ADMM to prior distribution mismatch, while also showing that the performance gap can be significantly reduced with only a few training samples from the desired distribution.} }
Endnote
%0 Conference Paper %T Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis %A Shirin Shoushtari %A Jiaming Liu %A Edward P. Chandler %A M. Salman Asif %A Ulugbek S. Kamilov %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-shoushtari24a %I PMLR %P 45154--45182 %U https://proceedings.mlr.press/v235/shoushtari24a.html %V 235 %X Plug-and-Play (PnP) priors is a widely-used family of methods for solving imaging inverse problems by integrating physical measurement models with image priors specified using image denoisers. PnP methods have been shown to achieve state-of-the-art performance when the prior is obtained using powerful deep denoisers. Despite extensive work on PnP, the topic of distribution mismatch between the training and testing data has often been overlooked in the PnP literature. This paper presents a set of new theoretical and numerical results on the topic of prior distribution mismatch and domain adaptation for the alternating direction method of multipliers (ADMM) variant of PnP. Our theoretical result provides an explicit error bound for PnP-ADMM due to the mismatch between the desired denoiser and the one used for inference. Our analysis contributes to the work in the area by considering the mismatch under nonconvex data-fidelity terms and expansive denoisers. Our first set of numerical results quantifies the impact of the prior distribution mismatch on the performance of PnP-ADMM on the problem of image super-resolution. Our second set of numerical results considers a simple and effective domain adaption strategy that closes the performance gap due to the use of mismatched denoisers. Our results suggest the relative robustness of PnP-ADMM to prior distribution mismatch, while also showing that the performance gap can be significantly reduced with only a few training samples from the desired distribution.
APA
Shoushtari, S., Liu, J., Chandler, E.P., Asif, M.S. & Kamilov, U.S.. (2024). Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:45154-45182 Available from https://proceedings.mlr.press/v235/shoushtari24a.html.

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