Compressive sensing of signals from a GMM with sparse precision matrices

Jianbo Yang, Xuejun Liao, Minhua Chen, Lawrence Carin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

This paper is concerned with compressive sensing of signals drawn from a Gaussian mixture model (GMM) with sparse precision matrices. Previous work has shown: (i) a signal drawn from a given GMM can be perfectly reconstructed from r noise-free measurements if the (dominant) rank of each covariance matrix is less than r; (ii) a sparse Gaussian graphical model can be efficiently estimated from fully-observed training signals using graphical lasso. This paper addresses a problem more challenging than both (i) and (ii), by assuming that the GMM is unknown and each signal is only observed through incomplete linear measurements. Under these challenging assumptions, we develop a hierarchical Bayesian method to simultaneously estimate the GMM and recover the signals using solely the incomplete measurements and a Bayesian shrinkage prior that promotes sparsity of the Gaussian precision matrices. In addition, we provide theoretical performance bounds to relate the reconstruction error to the number of signals for which measurements are available, the sparsity level of precision matrices, and the "incompleteness" of measurements. The proposed method is demonstrated extensively on compressive sensing of imagery and video, and the results with simulated and hardware-acquired real measurements show significant performance improvement over state-of-the-art methods.
Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
Pages3194-3202
Number of pages9
StatePublished - Jan 1 2014
Externally publishedYes

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