Abstract

We describe an approach to factor analysis/source separation for multi-channel image data where the sources are assumed to be Gaussian mixtures, which may be independent or dependent e.g. mixtures of multivariate Gaussians. An MCMC procedure has been developed that implements a fully Bayesian procedure e.g. it computes the posterior distribution of sources, their Gaussian mixture parameters and the matrix of linear coefficients from the data. The method is applied to recovery of the cosmic microwave background CMB ), being an example of source separation applied to image data. The CMB is one of many sources of extraterrestrial microwave radiation and we observe a weighted sum of these sources from the Earth at different frequencies. Its accurate reconstruction is of great interest to astronomers and physicists since knowledge of its properties, and in particular its anisotropies, will place strong restrictions on current cosmological theories. From the perspective of a Bayesian solution, this application is interesting as there is considerable prior information about the linear coefficients and the sources. Results from the analysis of data from the WMAP satellite will be presented, where microwave radiation is observed at 5 frequencies and separated into sources, including the CMB . A discussion of the many outstanding issues in this problem is also presented.