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Classification and Reconstruction of High-Dimensional Signals From Low-Dimensional Features in the Presence of Side Information

Renna, F; Wang, L; Yuan, X; Yang, J; Reeves, G; Calderbank, R; Carin, L; (2016) Classification and Reconstruction of High-Dimensional Signals From Low-Dimensional Features in the Presence of Side Information. IEEE Transactions on Information Theory , 62 (11) pp. 6459-6492. 10.1109/TIT.2016.2606646. Green open access

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Abstract

This paper offers a characterization of fundamental limits on the classification and reconstruction of high-dimensional signals from low-dimensional features, in the presence of side information. We consider a scenario where a decoder has access both to linear features of the signal of interest and to linear features of the side information signal; while the side information may be in a compressed form, the objective is recovery or classification of the primary signal, not the side information. The signal of interest and the side information are each assumed to have (distinct) latent discrete labels; conditioned on these two labels, the signal of interest and side information are drawn from a multivariate Gaussian distribution that correlates the two. With joint probabilities on the latent labels, the overall signal-(side information) representation is defined by a Gaussian mixture model. By considering bounds to the misclassification probability associated with the recovery of the underlying signal label, and bounds to the reconstruction error associated with the recovery of the signal of interest itself, we then provide sharp sufficient and/or necessary conditions for these quantities to approach zero when the covariance matrices of the Gaussians are nearly low rank. These conditions, which are reminiscent of the well-known Slepian-Wolf and Wyner-Ziv conditions, are the function of the number of linear features extracted from signal of interest, the number of linear features extracted from the side information signal, and the geometry of these signals and their interplay. Moreover, on assuming that the signal of interest and the side information obey such an approximately low-rank model, we derive the expansions of the reconstruction error as a function of the deviation from an exactly low-rank model; such expansions also allow the identification of operational regimes, where the impact of side information on signal reconstruction is most relevant. Our framework, which offers a principled mechanism to integrate side information in high-dimensional data problems, is also tested in the context of imaging applications. In particular, we report state-of-theart results in compressive hyperspectral imaging applications, where the accompanying side information is a conventional digital photograph.

Type: Article
Title: Classification and Reconstruction of High-Dimensional Signals From Low-Dimensional Features in the Presence of Side Information
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TIT.2016.2606646
Publisher version: http://doi.org/10.1109/TIT.2016.2606646
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/
Keywords: Science & Technology, Technology, Computer Science, Information Systems, Engineering, Electrical & Electronic, Computer Science, Engineering, Classification, reconstruction, Gaussian mixture models, diversity-order, MMSE, misclassification probability, side information, GAUSSIAN MIXTURE-MODELS, BLOCK-SPARSE SIGNALS, FEATURE-EXTRACTION, RANDOM PROJECTIONS, RECOVERY, FREQUENCY, REPRESENTATION, SUBSPACES, MANIFOLDS, CHANNELS
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1529740
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