Astrophysical data analysis using non-stationary signal processing techniques. 2009-2010 Final report

This report summarizes the research activities on non-stationary signal processing problems in cosmology in the framework of the CNR-CSIC bilateral research agreement. The participating laboratories are Signals and Images laboratory of ISTI-CNR and Istituto di Fisica Applicata di Cantabria, Santander. The activities in the project can be summarised under the following headings: 1) Diffuse component separation 1.1 Bayesian methods for diffuse component separation -Image separation with Markov random field models - Langevin sampling -Multiresolution source separation from convolutive mixtures -Space varying mixture separation 1.2. Dependent component analysis - general dependent component analysis - correlated component analysis 2) Compact source detection - Sparsity modelling of point sources and detection - Time-frequency detection - Bayesian detection 3) Future directions - Simulations on real data (WMAP, Planck) - Point source detection via Reversible Jump MCMC The project aimed at solving crucial signal processing problems that are encountered in the Planck satellite mission. The theoretical contributions are in the development of novel non-stationary image separation and Bayesian signal detection methods. We hope the methodogies developed in this project to be useful in the analysis of the Planck data.