Uncertainty Modeling in Generative Compressed Sensing

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.

Automated summary

This paper presents a novel method called CS-BGM that effectively expands the range of generator in generative compressed sensing. The method introduces uncertainties to the latent variable and parameters of the generator while adopting variational inference and maximum a posteriori to infer them. Theoretical analysis and extensive experiments demonstrate the improvement of CS-BGM over baselines.