In pursuit of the big-bang signature: Bayesian separation of components in astrophysical radiation maps

Kuruoglu E. E.

Source separation  Astrophysical microwave radiation images 

In this work we present our research into the separation of astrophysical components using numerical Bayesian techniques. The work is motivated by the Planck satellite project. ESA's Planck satellite, which is to be launched in 2007, will provide 9 all-sky maps ranging in frequency from 30 GHz to 900 GHz, and in angular resolution from 30 to 4.5 arcminutes. Celestial microwave radiation is generated by various astronomical sources, and the measured signals are superimpositions of the source signals, corrupted by measurement noise. Source signals include the cosmic microwave background (CMB), the thermal Galactic dust radiation, the synchrotron radiation (caused by the interaction of the electrons with magnetic field of the galaxy) and the free-free radiation (due to the thermal bremstrahlung from hot electrons when accelarated by ions in the interstellar gas); among which CMB is of paramount importance since it is a relic radiation remaining from the first instant light was able to travel in the universe and therefore contains the picture of the very early universe. In addition, the measurement of the anisotropies in the CMB will place fundamental constraints on models for the evolution of large scale structure in the universe. Each of the other source signals is also of interest in cosmology and astrophysics. Our goal is to reconstruct these signals. We implement first a Markov Chain Monte Carlo (MCMC) algorithm to perform Bayesian source separation, with application to the separation of signals of different origin in sky radiation maps. The problem is formulated as the separation of an instantaneous linear mixing. Since the MCMC methods provide samples from the full posterior distribution, one can easily infer other functions of the parameters and their uncertainities. The great flexibility of the sampling approach allows us to make appropriate modelling choices for our problem. In particular, we have used a Gibbs sampling scheme and have adopted a Gaussian mixture model for the sources. We also note that antenna noise is Gaussian but non-stationary, with a different but known variance at each pixel.To accommodate the nonstationarity in the noise and the signals, we then extend the work to sequential Monte Carlo techniques. Particle filtering gives significantly better results which will be presented at the conference.

Source: Valencia International Meetings on Bayesian Statistics, Valencia, Spain, 01-06/06/2006