Bayesian subspace estimation using CS decomposition

Subspace estimation using relatively few samples is a frequently encountered problem in numerous applications, including hyperspectral imagery the target application of this paper. We address this problem in a Bayesian framework assuming that some rough prior knowledge about the subspace is available. Our approach is based on the CS decomposition of an orthogonal matrix whose columns span the subspace of interest. This parametrization only involves mild assumptions about the distribution of the angles between the actual subspace and the prior subspace, and is intuitively appealing. We derive the posterior distribution for the matrices involved in the CS decomposition and the angles between subspaces, and we propose a Gibbs sampling scheme to compute the minimum mean-square distance estimator of the subspace of interest. The estimator accuracy is evaluated through numerical simulations and tested against real hyperspectral data.