Equivariant Priors for compressed sensing with unknown orientation

Anna Kuzina, Kumar Pratik, Fabio Valerio Massoli, Arash Behboodi
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:11753-11771, 2022.

Abstract

In compressed sensing, the goal is to reconstruct the signal from an underdetermined system of linear measurements. Thus, prior knowledge about the signal of interest and its structure is required. Additionally, in many scenarios, the signal has an unknown orientation prior to measurements. To address such recovery problems, we propose using equivariant generative models as a prior, which encapsulate orientation information in their latent space. Thereby, we show that signals with unknown orientations can be recovered with iterative gradient descent on the latent space of these models and provide additional theoretical recovery guarantees. We construct an equivariant variational autoencoder and use the decoder as generative prior for compressed sensing. We discuss additional potential gains of the proposed approach in terms of convergence and latency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-kuzina22a, title = {Equivariant Priors for compressed sensing with unknown orientation}, author = {Kuzina, Anna and Pratik, Kumar and Massoli, Fabio Valerio and Behboodi, Arash}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {11753--11771}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/kuzina22a/kuzina22a.pdf}, url = {https://proceedings.mlr.press/v162/kuzina22a.html}, abstract = {In compressed sensing, the goal is to reconstruct the signal from an underdetermined system of linear measurements. Thus, prior knowledge about the signal of interest and its structure is required. Additionally, in many scenarios, the signal has an unknown orientation prior to measurements. To address such recovery problems, we propose using equivariant generative models as a prior, which encapsulate orientation information in their latent space. Thereby, we show that signals with unknown orientations can be recovered with iterative gradient descent on the latent space of these models and provide additional theoretical recovery guarantees. We construct an equivariant variational autoencoder and use the decoder as generative prior for compressed sensing. We discuss additional potential gains of the proposed approach in terms of convergence and latency.} }
Endnote
%0 Conference Paper %T Equivariant Priors for compressed sensing with unknown orientation %A Anna Kuzina %A Kumar Pratik %A Fabio Valerio Massoli %A Arash Behboodi %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-kuzina22a %I PMLR %P 11753--11771 %U https://proceedings.mlr.press/v162/kuzina22a.html %V 162 %X In compressed sensing, the goal is to reconstruct the signal from an underdetermined system of linear measurements. Thus, prior knowledge about the signal of interest and its structure is required. Additionally, in many scenarios, the signal has an unknown orientation prior to measurements. To address such recovery problems, we propose using equivariant generative models as a prior, which encapsulate orientation information in their latent space. Thereby, we show that signals with unknown orientations can be recovered with iterative gradient descent on the latent space of these models and provide additional theoretical recovery guarantees. We construct an equivariant variational autoencoder and use the decoder as generative prior for compressed sensing. We discuss additional potential gains of the proposed approach in terms of convergence and latency.
APA
Kuzina, A., Pratik, K., Massoli, F.V. & Behboodi, A.. (2022). Equivariant Priors for compressed sensing with unknown orientation. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:11753-11771 Available from https://proceedings.mlr.press/v162/kuzina22a.html.

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