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Joint Bayesian estimation of close subspaces from noisy measurements

Besson, Olivier and Dobigeon, Nicolas and Tourneret, Jean-Yves Joint Bayesian estimation of close subspaces from noisy measurements. (2014) IEEE Signal Processing Letters, 21 (2). 168-171. ISSN 1070-9908

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Official URL: http://dx.doi.org/10.1109/LSP.2013.2296138


In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue reminiscent of the well-known Procrustes problem. A Bayesian approach is investigated where the subspaces of interest are considered as random with a joint prior distribution (namely a Bingham distribution), which allows the closeness of the two subspaces to be parameterized. Within this framework, the minimum mean-square distance estimator of both subspaces is formulated and implemented via a Gibbs sampler. A simpler scheme based on alternative maximum a posteriori estimation is also presented. The new schemes are shown to provide more accurate estimates of the angles between the subspaces, compared to singular value decomposition based independent estimation of the two subspaces.

Item Type:Article
Additional Information:Thanks to IEEE editor. The original publication is available at http://ieeexplore.ieee.org
HAL Id:hal-00924988
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Laboratory name:
Deposited On:07 Jan 2014 12:47

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