Nicolas Dobigeon
Minimum mean square distance estimation of a subspace.
Wed, 01/19/2011 - 16:01 — SomNambulAuthors: Nicolas Dobigeon, Jean-Yves Tourneret, Olivier Besson
Subjects: Methodology
AbstractWe consider the problem of subspace estimation in a Bayesian setting. Since
we are operating in the Grassmann manifold, the usual approach which consists
of minimizing the mean square error (MSE) between the true subspace $U$ and its
estimate $\hat{U}$ may not be adequate as the MSE is not the natural metric in
the Grassmann manifold. As an alternative, we propose to carry out subspace
estimation by minimizing the mean square distance (MSD) between $U$ and its
estimate, where the considered distance is a natural metric in the Grassmann
manifold, viz.Enhancing hyperspectral image unmixing with spatial correlations.
Fri, 02/05/2010 - 16:01 — SomNambulAuthors: Nicolas Dobigeon, Jean-Yves Tourneret, Olivier Eches
Subjects: Methodology
AbstractThis paper describes a new algorithm for hyperspectral image unmixing. Most
of the unmixing algorithms proposed in the literature do not take into account
the possible spatial correlations between the pixels. In this work, a Bayesian
model is introduced to exploit these correlations. The image to be unmixed is
assumed to be partitioned into regions (or classes) where the statistical
properties of the abundance coefficients are homogeneous. A Markov random field
is then proposed to model the spatial dependency of the pixels within any
class.Bayesian separation of spectral sources under non-negativity and full additivity constraints.
Thu, 09/24/2009 - 12:35 — SomNambulAuthors: Nicolas Dobigeon, Jean-Yves Tourneret, Said Moussaoui, Cedric Carteret
Subjects: Methodology
AbstractThis paper addresses the problem of separating spectral sources which are
linearly mixed with unknown proportions. The main difficulty of the problem is
to ensure the full additivity (sum-to-one) of the mixing coefficients and
non-negativity of sources and mixing coefficients. A Bayesian estimation
approach based on Gamma priors was recently proposed to handle the
non-negativity constraints in a linear mixture model. However, incorporating
the full additivity constraint requires further developments.Bayesian orthogonal component analysis for sparse representation.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: Nicolas Dobigeon, Jean-Yves Tourneret
Subjects: Methodology
AbstractThis paper addresses the problem of identifying a lower dimensional space
where observed data can be sparsely represented. This under-complete dictionary
learning task can be formulated as a blind separation problem of sparse sources
linearly mixed with an unknown orthogonal mixing matrix. This issue is
formulated in a Bayesian framework. First, the unknown sparse sources are
modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted
mixture of an atom at zero and a Gaussian distribution is proposed as prior
distribution for the unobserved sources.
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