4,406 research outputs found
On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation
International audienceThe surface of Mars is currently being imaged with an unprecedented combination of spectral and spatial resolution. This high resolution, and its spectral range, gives the ability to pinpoint chemical species on the surface and the atmosphere of Mars more accurately than before. The subject of this paper is to present a method to extract informations on these chemicals from hyperspectral images. A first approach, based on independent component analysis (ICA) [P. Comon, Independent component analysis, a new concept? Signal Process. 36 (3) (1994) 287-314], is able to extract artifacts and locations of CO2 and H2O ices. However, the main independence assumption and some basic properties (like the positivity of images and spectra) being unverified, the reliability of all the independent components (ICs) is weak. For improving the component extraction and consequently the endmember classification, a combination of spatial ICA with spectral Bayesian positive source separation (BPSS) [S. Moussaoui, D. Brie, A. Mohammad-Djafari, C. Carteret, Separation of non-negative mixture of non-negative sources using a Bayesian approach and MCMC sampling, IEEE Trans. Signal Process. 54 (11) (2006) 4133-4145] is proposed. To reduce the computational burden, the basic idea is to use spatial ICA yielding a rough classification of pixels, which allows selection of small, but relevant, number of pixels. Then, BPSS is applied for the estimation of the source spectra using the spectral mixtures provided by this reduced set of pixels. Finally, the abundances of the components are assessed on the whole pixels of the images. Results of this approach are shown and evaluated by comparison with available reference spectra
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
Implementation strategies for hyperspectral unmixing using Bayesian source separation
Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach
for hyperspectral data unmixing, where numerical non-negativity of spectra and
abundances has to be ensured, such in remote sensing. Moreover, it is sensible
to impose a sum-to-one (full additivity) constraint to the estimated source
abundances in each pixel. Even though non-negativity and full additivity are
two necessary properties to get physically interpretable results, the use of
BPSS algorithms has been so far limited by high computation time and large
memory requirements due to the Markov chain Monte Carlo calculations. An
implementation strategy which allows one to apply these algorithms on a full
hyperspectral image, as typical in Earth and Planetary Science, is introduced.
Effects of pixel selection, the impact of such sampling on the relevance of the
estimated component spectra and abundance maps, as well as on the computation
times, are discussed. For that purpose, two different dataset have been used: a
synthetic one and a real hyperspectral image from Mars.Comment: 10 pages, 6 figures, submitted to IEEE Transactions on Geoscience and
Remote Sensing in the special issue on Hyperspectral Image and Signal
Processing (WHISPERS
Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery
This paper studies a fully Bayesian algorithm for endmember extraction and
abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral
image is decomposed as a linear combination of pure endmember spectra following
the linear mixing model. The estimation of the unknown endmember spectra is
conducted in a unified manner by generating the posterior distribution of
abundances and endmember parameters under a hierarchical Bayesian model. This
model assumes conjugate prior distributions for these parameters, accounts for
non-negativity and full-additivity constraints, and exploits the fact that the
endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is
proposed to overcome the complexity of evaluating the resulting posterior
distribution. This sampler generates samples distributed according to the
posterior distribution and estimates the unknown parameters using these
generated samples. The accuracy of the joint Bayesian estimator is illustrated
by simulations conducted on synthetic and real AVIRIS images
Approximate Inference for Constructing Astronomical Catalogs from Images
We present a new, fully generative model for constructing astronomical
catalogs from optical telescope image sets. Each pixel intensity is treated as
a random variable with parameters that depend on the latent properties of stars
and galaxies. These latent properties are themselves modeled as random. We
compare two procedures for posterior inference. One procedure is based on
Markov chain Monte Carlo (MCMC) while the other is based on variational
inference (VI). The MCMC procedure excels at quantifying uncertainty, while the
VI procedure is 1000 times faster. On a supercomputer, the VI procedure
efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50
terabytes of images in 14.6 minutes, demonstrating the scaling characteristics
necessary to construct catalogs for upcoming astronomical surveys.Comment: accepted to the Annals of Applied Statistic
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
Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps
We propose to model the image differentials of astrophysical source maps by
Student's t-distribution and to use them in the Bayesian source separation
method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC)
sampling scheme to unmix the astrophysical sources and describe the derivation
details. In this scheme, we use the Langevin stochastic equation for
transitions, which enables parallel drawing of random samples from the
posterior, and reduces the computation time significantly (by two orders of
magnitude). In addition, Student's t-distribution parameters are updated
throughout the iterations. The results on astrophysical source separation are
assessed with two performance criteria defined in the pixel and the frequency
domains.Comment: 12 pages, 6 figure
Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery
This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data
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