Sparsity and cosmology: inverse problems in cosmic microwave background experiments

Abstract

We propose a new method to better estimate and subtract the contribution of detected compact sources to the microwave sky. These bright compact source emissions contaminate the full-sky data over a significant fraction of the sky, and should therefore be accurately removed if a high resolution and full-sky estimate of the components is sought after. However the point source spectral variability hampers accurate blind source separation, even with state-of-the-art localized source separation techniques. In this work, we rather propose to estimate the flux of the brightest compact sources using a morphological separation approach, relying on a more sophisticated model for the background than in standard approaches. Essentially, this amounts to separate point sources with known support and shape from a background assumed sparse in the spherical harmonic domain. This approach is compared to standard local χ 2 minimization modeling the background as a low order polynomial on WMAP realistic simulations. If in noisy situations estimating more than a few parameter does not improve flux recovery, in the first WMAP channels the proposed method leads to lower biases (typically by factors of 2) and increased robustness.