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

FRAMEWORK FOR ONLINE SUPERIMPOSED EVENT DETECTION BY SEQUENTIAL MONTE CARLO

In this paper, we consider online seperation and detection of superimposed events by applying particle filtering. We concentrate on a model where a background process, represented by a 1D-signal, is superimposed by an Auto-Regressive (AR) ’event signal’, but the proposed approach is applicable in a more general setting. The activation and deactivation times of the event-signal are assumed to be unknown. We solve the online detection problem of this superpositional event by extending the state space dimension by one. The additional parameter of the state represents the AR-signal, which is zero when deactivated. Numerical experiments demonstrate the effectiveness of our approach

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 13, NO. 4, APRIL 2004 527 Modeling SAR Images With a

Synthetic aperture radar (SAR) imagery has found important applications due to its clear advantages over optical satellite imagery one of them being able to operate in various weather conditions. However, due to the physics of the radar imaging process, SAR images contain unwanted artifacts in the form of a granular look which is called speckle. The assumptions of the classical SAR image generation model lead to a Rayleigh distribution model for the histogram of the SAR image. However, some experimental data such as images of urban areas show impulsive characteristics that correspond to underlying heavy-tailed distributions, which are clearly non-Rayleigh. Some alternative distributions have been suggested such as the Weibull, log-normal, and the k-distribution which had success in varying degrees depending on the application. Recently, an alternative model namely the-stable distribution has been suggested for modeling radar clutter. In this paper, we show that the amplitude distribution of the complex wave, the real and the imaginery components of which are assumed to be distributed by the-stable distribution, is a generalization of the Rayleigh distribution. We demonstrate that the amplitude distribution is a mixture of Rayleighs as is the k-distribution in accordance with earlier work on modeling SAR images which showed that almost all successful SAR image models could be expressed as mixtures of Rayleighs. We also present parameter estimation techniques based on negative order moments for the new model. Finally, we test the performance of the model on urban images and compare with other models such as Rayleigh, Weibull, and the k-distribution

Astrophysical Source Separation

In this work, we will confront the problem of source separation in the field of astrophysics, where the contributions of various Galactic and extra-Galactic components need to be separated from a set of observed noisy mixtures. Most of the previous work on the problem perform blind source separation, assume noiseless models, and in the few cases when noise is taken into account assume Gaussianity and spaceinvariance