Solving Inverse Problems with a Flow-based Noise Model

Jay Whang, Qi Lei, Alex Dimakis
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:11146-11157, 2021.

Abstract

We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with arbitrary dependencies as well as non-linear forward operators. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns. We also present initial theoretical recovery guarantees for solving inverse problems with a flow prior.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-whang21a, title = {Solving Inverse Problems with a Flow-based Noise Model}, author = {Whang, Jay and Lei, Qi and Dimakis, Alex}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {11146--11157}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/whang21a/whang21a.pdf}, url = {https://proceedings.mlr.press/v139/whang21a.html}, abstract = {We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with arbitrary dependencies as well as non-linear forward operators. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns. We also present initial theoretical recovery guarantees for solving inverse problems with a flow prior.} }
Endnote
%0 Conference Paper %T Solving Inverse Problems with a Flow-based Noise Model %A Jay Whang %A Qi Lei %A Alex Dimakis %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-whang21a %I PMLR %P 11146--11157 %U https://proceedings.mlr.press/v139/whang21a.html %V 139 %X We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with arbitrary dependencies as well as non-linear forward operators. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns. We also present initial theoretical recovery guarantees for solving inverse problems with a flow prior.
APA
Whang, J., Lei, Q. & Dimakis, A.. (2021). Solving Inverse Problems with a Flow-based Noise Model. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:11146-11157 Available from https://proceedings.mlr.press/v139/whang21a.html.

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