Et Aveugles En Traitement Du Signal Et Des Images

We consider the problem of subspace estimation in aBayesian setting. Since we are operating in the Grassmann man-ifold, the usual approach which consists of minimizing the meansquare error (MSE) between the true subspace and its estimatemay not be adequate as the MSE is not the natural metric in theGrassmann manifold , i.e., the set of -dimensional subspacesin . As an alternative, we propose to carry out subspace esti-mation by minimizing the mean square distance between andits estimate, where the considered distance is a natural metric inthe Grassmann manifold, viz. the distance between the projectionmatrices. We show that the resulting estimator is no longer the pos-terior mean of but entails computing the principal eigenvectorsof the posterior mean of . Derivation of the minimum meansquare distance (MMSD) estimator is carried out in a few illus-trative examples including a linear Gaussian model for the dataand Bingham or von Mises Fisher prior distributions for . In allscenarios, posterior distributions are derived and the MMSD esti-mator is obtained either analytically or implemented via a Markovchain Monte Carlo simulation method. The method is shown toprovide accurate estimates even when the number of samples islower than the dimension of . An application to hyperspectralimagery is finally investigated.