On the separation of T Tauri star spectra using non-negative matrix factorization and Bayesian positive source separation

The objective of this study is to compare and evaluate Bayesian and deterministic methods of positive source separation of young star spectra. In the Bayesian approach, the proposed Bayesian Positive Source Separation (BPSS) method uses Gamma priors to enforce non-negativity in the source signals and mixing coefficients and a Markov Chain Monte Carlo (MCMC) algorithm, modified by suggesting simpler proposal distributions and randomly initializing the MCMC to correctly separate spectra. In the deterministic approach, two Non-negative Matrix Factorization (NNMF) algorithms, the multiplicative update rule algorithm and an alternating least squares algorithm, are used to separate the star spectra into sources. The BPSS and NNMF algorithms are applied to the field of Astrophysics by applying the source separation techniques to T Tauri star spectra, resulting in a successful decomposition of the spectra into their sources. These methods are for the first time being applied and evaluated in optical spectroscopy. The results show that, while both methods perform well, BPSS outperforms NNMF. The NNMF and BPSS algorithms improve upon the current methodology used in Astrophysics iu two important ways. First, they permit the identification of additional components of the spectra in addition to the photosphere and boundary layer which can be modeled with current methods. Second, by applying a statistical algorithm, the modeling of T Tauri stars becomes less subjective. These methods may be further extrapolated to model spectra from other types of stars or astrophysical phenomena

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

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

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

Bayesian source separation of fMRI signals

In analyzing the results of functional magnetic resonance imaging, the identification of significant activation in voxels is a crucial task. In computing the activation level, a standard method is to select an assumed to be known reference function and perform a multiple regression of the time courses on it and a linear trend. Once the linear trend is found, the correlation between the assumed to be known reference function and the detrended observed time-course in each voxel is computed and voxels colored according to their correlation. But the most important question is: How do we choose the reference function? This paper develops a Bayesian statistical approach to determining the underlying source reference function based on Bayesian source separation, and uses it on both simulated and real fMRI data. This underlying reference function is the unobserved response due the presentation of the experimental stimulus

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

Gravitational detection of a low-mass dark satellite at cosmological distance

The mass-function of dwarf satellite galaxies that are observed around Local Group galaxies substantially differs from simulations based on cold dark matter: the simulations predict many more dwarf galaxies than are seen. The Local Group, however, may be anomalous in this regard. A massive dark satellite in an early-type lens galaxy at z = 0.222 was recently found using a new method based on gravitational lensing, suggesting that the mass fraction contained in substructure could be higher than is predicted from simulations. The lack of very low mass detections, however, prohibited any constraint on their mass function. Here we report the presence of a 1.9 +/- 0.1 x 10^8 M_sun dark satellite in the Einstein-ring system JVAS B1938+666 at z = 0.881, where M_sun denotes solar mass. This satellite galaxy has a mass similar to the Sagittarius galaxy, which is a satellite of the Milky Way. We determine the logarithmic slope of the mass function for substructure beyond the local Universe to be alpha = 1.1^+0.6_-0.4, with an average mass-fraction of f = 3.3^+3.6_-1.8 %, by combining data on both of these recently discovered galaxies. Our results are consistent with the predictions from cold dark matter simulations at the 95 per cent confidence level, and therefore agree with the view that galaxies formed hierarchically in a Universe composed of cold dark matter.Comment: 25 pages, 7 figures, accepted for publication in Nature (19 January 2012