5,354 research outputs found
Bayesian separation of spectral sources under non-negativity and full additivity constraints
This 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. This paper
studies a new hierarchical Bayesian model appropriate to the non-negativity and
sum-to-one constraints associated to the regressors and regression coefficients
of linear mixtures. The estimation of the unknown parameters of this model is
performed using samples generated using an appropriate Gibbs sampler. The
performance of the proposed algorithm is evaluated through simulation results
conducted on synthetic mixture models. The proposed approach is also applied to
the processing of multicomponent chemical mixtures resulting from Raman
spectroscopy.Comment: v4: minor grammatical changes; Signal Processing, 200
Image Reconstruction in Optical Interferometry
This tutorial paper describes the problem of image reconstruction from
interferometric data with a particular focus on the specific problems
encountered at optical (visible/IR) wavelengths. The challenging issues in
image reconstruction from interferometric data are introduced in the general
framework of inverse problem approach. This framework is then used to describe
existing image reconstruction algorithms in radio interferometry and the new
methods specifically developed for optical interferometry.Comment: accepted for publication in IEEE Signal Processing Magazin
A stochastic algorithm for probabilistic independent component analysis
The decomposition of a sample of images on a relevant subspace is a recurrent
problem in many different fields from Computer Vision to medical image
analysis. We propose in this paper a new learning principle and implementation
of the generative decomposition model generally known as noisy ICA (for
independent component analysis) based on the SAEM algorithm, which is a
versatile stochastic approximation of the standard EM algorithm. We demonstrate
the applicability of the method on a large range of decomposition models and
illustrate the developments with experimental results on various data sets.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS499 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bayesian orthogonal component analysis for sparse representation
This 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. A non-informative prior distribution
defined on an appropriate Stiefel manifold is elected for the mixing matrix.
The Bayesian inference on the unknown parameters is conducted using a Markov
chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is
designed to generate samples asymptotically distributed according to the joint
posterior distribution of the unknown model parameters and hyperparameters.
These samples are then used to approximate the joint maximum a posteriori
estimator of the sources and mixing matrix. Simulations conducted on synthetic
data are reported to illustrate the performance of the method for recovering
sparse representations. An application to sparse coding on under-complete
dictionary is finally investigated.Comment: Revised version. Accepted to IEEE Trans. Signal Processin
Supervised nonlinear spectral unmixing using a post-nonlinear mixing model for hyperspectral imagery
This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data
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