A minimax entropy method for blind separation of dependent components in astrophysical images

We develop a new technique for blind separation of potentially non independent components in astrophysical images. Given a set of linearly mixed images, corresponding to different measurement channels, we estimate the original electromagnetic radiation sources in a blind fashion. Specifically, we investigate the separation of cosmic microwave background (CMB), thermal dust and galactic synchrotron emissions without imposing any assumption on the mixing matrix. In our approach, we use the Gaussian and non-Gaussian features of astrophysical sources and we assume that CMB-dust and CMB-synchrotron are uncorrelated pairs while dust and synchrotron are correlated which is in agreement with theory. These assumptions allow us to develop an algorithm which associates the Minimum Entropy solutions with the non-Gaussian sources (thermal dust and galactic synchrotron emissions) and the Maximum Entropy solution as the only Gaussian source which is the CMB. This new method is more appropriate than ICA algorithms because independence between sources is not imposed which is a more realistic situation. We investigate two specific measures associated with entropy: Gaussianity Measure (GM) and Shannon Entropy (SE) and we compare them. Finally, we present a complete set of examples of separation using these two measures validating our approach and showing that it performs better than FastICA algorithm. The experimental results presented here were performed on an image database that simulates the measurements expected from the instruments that will operate onboard ESA's Planck Surveyor Satellite to measure the CMB anisotropies all over the celestial sphere.