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CS decomposition based Bayesian subspace estimation

Besson, Olivier and Dobigeon, Nicolas and Tourneret, Jean-Yves CS decomposition based Bayesian subspace estimation. (2012) IEEE Transactions on Signal Processing, vol. 60 (n° 8). pp. 4210-4218. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2012.2197619

Abstract

In numerous applications, it is required to estimate the principal subspace of the data, possibly from a very limited number of samples. Additionally, it often occurs that some rough knowledge about this subspace is available and could be used to improve subspace estimation accuracy in this case. This is the problem we address herein and, in order to solve it, a Bayesian approach is proposed. The main idea consists of using the CS decomposition of the semi-orthogonal matrix $\bH$ whose columns span the subspace of interest. This parametrization is intuitively appealing and allows for non informative prior distributions of the matrices involved in the CS decomposition and very mild assumptions about the angles between the actual subspace and the prior subspace. The posterior distributions are derived and a Gibbs sampling scheme is presented to obtain the minimum mean-square distance estimator of the subspace of interest. Numerical simulations and an application to real hyperspectral data assess the validity and the performances of the estimator.

Item Type:Article
Additional Information:Thanks to IEEE editor. (c) 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. The definitive version is available at http://ieeexplore.ieee.org
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE
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Deposited By: Olivier Besson
Deposited On:18 Jul 2012 12:26

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