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

A Bayesian approach to the study of white dwarf binaries in LISA data: The application of a reversible jump Markov chain Monte Carlo method

The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals "out of the box'', handling the total number of signals as an additional unknown parameter beside the unknown parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals.Comment: 18 pages, 9 figures, 3 tables, accepted for publication in PRD, revised versio

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

BayesWave: Bayesian Inference for Gravitational Wave Bursts and Instrument Glitches

A central challenge in Gravitational Wave Astronomy is identifying weak signals in the presence of non-stationary and non-Gaussian noise. The separation of gravitational wave signals from noise requires good models for both. When accurate signal models are available, such as for binary Neutron star systems, it is possible to make robust detection statements even when the noise is poorly understood. In contrast, searches for "un-modeled" transient signals are strongly impacted by the methods used to characterize the noise. Here we take a Bayesian approach and introduce a multi-component, variable dimension, parameterized noise model that explicitly accounts for non-stationarity and non-Gaussianity in data from interferometric gravitational wave detectors. Instrumental transients (glitches) and burst sources of gravitational waves are modeled using a Morlet-Gabor continuous wavelet frame. The number and placement of the wavelets is determined by a trans-dimensional Reversible Jump Markov Chain Monte Carlo algorithm. The Gaussian component of the noise and sharp line features in the noise spectrum are modeled using the BayesLine algorithm, which operates in concert with the wavelet model.Comment: 36 pages, 15 figures, Version accepted by Class. Quant. Gra

A Fixed-lag Particle Filter for the Joint Detection/Compensation of Interference Effects in GPS Navigation

Interferences are among the most penalizing error sources in Global Positioning System (GPS) navigation. So far, many effort has been devoted to developing GPS receivers more robust to the radiofrequency environment. Contrary to previous approaches, this paper does not aim at improving the estimation of the GPS pseudoranges between the mobile and the GPS satellites in the presence of interferences. As an alternative, we propose to model interference effects as variance jumps affecting the GPS measurements which can be directly detected and compensated at the level of the navigation algorithm. Since the joint detection/estimation of the interference errors and motion parameters is a highly non linear problem, a particle filtering technique is used. An original particle filter is developed to improve the detection performance while ensuring a good accuracy of the positioning solution

Algorithmes bayésiens pour le démélange supervisé, semi-supervisé et non-supervisé d’images hyperspectrales

Cet article présente des algorithmes totalement bayésiens pour le démélange d’images hyperspectrales. Chaque pixel de l’image est décomposée selon une combinaison de spectres de références pondérés par des coefficients d’abondances selon un modèle de mélange linéaire. Dans un cadre supervisé, nous supposons connus les spectres de références. Le problème consiste alors à estimer les coefficients du mélange sous des contraintes de positivité et d’additivité. Une loi a priori adéquate est choisie pour ces coefficients qui sont estimés à partir de leur loi a posteriori. Un algorithme de Monte Carlo par chaîne de Markov (MCMC) est développé pour approcher les estimateurs. Dans un cadre semi-supervisé, les spectres participant au mélange seront supposés inconnus. Nous faisons l’hypothèse qu’ils appartiennent à une bibliothèque spectrale. Un algorithme MCMC à sauts réversibles permet dans ce cas de résoudre le problème de sélection de modèle. Enfin, dans un dernier cadre d’étude, les algorithmes précédents sont étendus au démélange non-supervisé d’images hyperspectrales, c’est-à-dire au problème d’estimation conjointe des spectres et des coefficients de mélange. Ce problème de séparation aveugle de sources est résolu dans un sous-espace approprié