Abstract
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies between the components of the sparse signal of interest. A hierarchical Gaussian process describes such structure and the interdependencies are represented via the covariance matrices of the prior distributions. The inference is based on the expectation propagation method and the theoretical derivation of the posterior distribution is provided in this paper. The inference framework is thoroughly evaluated over synthetic, real video, and electroencephalography (EEG) data where the spatio-temporal evolving patterns need to be reconstructed with high accuracy. It is shown that it achieves 15% improvement of the F-measure compared with the alternating direction method of multipliers, spatio-temporal sparse Bayesian learning method and the one-level Gaussian process model. Additionally, the required memory for the proposed algorithm is less than in the one-level Gaussian process model. This structured sparse regression framework is of broad applicability to source localization and object detection problems with sparse signals.
Original language | English |
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Pages (from-to) | 4598-4611 |
Number of pages | 14 |
Journal | IEEE Transactions on Signal Processing |
Volume | 66 |
Issue number | 17 |
Early online date | 23 Jul 2018 |
DOIs | |
Publication status | Published - 1 Sept 2018 |
Funding
Manuscript received January 9, 2018; revised April 20, 2018 and June 25, 2018; accepted July 9, 2018. Date of publication July 23, 2018; date of current version July 31, 2018. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Wenwu Wang. This work was supported by the EC Seventh Framework Programme [FP7 2013-2017] TRAcking in compleX sensor systems under Grant 607400. (Corresponding author: Danil Kuzin.) D. Kuzin and L. Mihaylova are with the Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, U.K. (e-mail:, [email protected]; [email protected]).
Keywords
- Bayes methods
- biomedical imaging
- Compressed sensing
- Gaussian processes
- object detection