Uncertainty Modeling in Generative Compressed Sensing

Yilang Zhang, Mengchu Xu, Xiaojun Mao, Jian Wang
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:26655-26668, 2022.

Abstract

Compressed sensing (CS) aims to recover a high-dimensional signal with structural priors from its low-dimensional linear measurements. Inspired by the huge success of deep neural networks in modeling the priors of natural signals, generative neural networks have been recently used to replace the hand-crafted structural priors in CS. However, the reconstruction capability of the generative model is fundamentally limited by the range of its generator, typically a small subset of the signal space of interest. To break this bottleneck and thus reconstruct those out-of-range signals, this paper presents a novel method called CS-BGM that can effectively expands the range of generator. Specifically, CS-BGM introduces uncertainties to the latent variable and parameters of the generator, while adopting the variational inference (VI) and maximum a posteriori (MAP) to infer them. Theoretical analysis demonstrates that expanding the range of generators is necessary for reducing the reconstruction error in generative CS. Extensive experiments show a consistent improvement of CS-BGM over the baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-zhang22ai, title = {Uncertainty Modeling in Generative Compressed Sensing}, author = {Zhang, Yilang and Xu, Mengchu and Mao, Xiaojun and Wang, Jian}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {26655--26668}, 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/zhang22ai/zhang22ai.pdf}, url = {https://proceedings.mlr.press/v162/zhang22ai.html}, abstract = {Compressed sensing (CS) aims to recover a high-dimensional signal with structural priors from its low-dimensional linear measurements. Inspired by the huge success of deep neural networks in modeling the priors of natural signals, generative neural networks have been recently used to replace the hand-crafted structural priors in CS. However, the reconstruction capability of the generative model is fundamentally limited by the range of its generator, typically a small subset of the signal space of interest. To break this bottleneck and thus reconstruct those out-of-range signals, this paper presents a novel method called CS-BGM that can effectively expands the range of generator. Specifically, CS-BGM introduces uncertainties to the latent variable and parameters of the generator, while adopting the variational inference (VI) and maximum a posteriori (MAP) to infer them. Theoretical analysis demonstrates that expanding the range of generators is necessary for reducing the reconstruction error in generative CS. Extensive experiments show a consistent improvement of CS-BGM over the baselines.} }
Endnote
%0 Conference Paper %T Uncertainty Modeling in Generative Compressed Sensing %A Yilang Zhang %A Mengchu Xu %A Xiaojun Mao %A Jian Wang %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-zhang22ai %I PMLR %P 26655--26668 %U https://proceedings.mlr.press/v162/zhang22ai.html %V 162 %X Compressed sensing (CS) aims to recover a high-dimensional signal with structural priors from its low-dimensional linear measurements. Inspired by the huge success of deep neural networks in modeling the priors of natural signals, generative neural networks have been recently used to replace the hand-crafted structural priors in CS. However, the reconstruction capability of the generative model is fundamentally limited by the range of its generator, typically a small subset of the signal space of interest. To break this bottleneck and thus reconstruct those out-of-range signals, this paper presents a novel method called CS-BGM that can effectively expands the range of generator. Specifically, CS-BGM introduces uncertainties to the latent variable and parameters of the generator, while adopting the variational inference (VI) and maximum a posteriori (MAP) to infer them. Theoretical analysis demonstrates that expanding the range of generators is necessary for reducing the reconstruction error in generative CS. Extensive experiments show a consistent improvement of CS-BGM over the baselines.
APA
Zhang, Y., Xu, M., Mao, X. & Wang, J.. (2022). Uncertainty Modeling in Generative Compressed Sensing. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:26655-26668 Available from https://proceedings.mlr.press/v162/zhang22ai.html.

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