  Missions such as WMAP or Planck measure full-sky fluctuations of the cosmic
microwave background and foregrounds, among which bright compact source
emissions cover a significant fraction of the sky. To accurately estimate the
diffuse components, the point-source emissions need to be separated from the
data, which requires a dedicated processing. We propose a new technique to
estimate the flux of the brightest point sources using a morphological
separation approach: point sources with known support and shape are separated
from diffuse emissions that are assumed to be sparse in the spherical harmonic
domain. This approach is compared on both WMAP simulations and data with the
standard local chi2 minimization, modelling the background as a low-order
polynomial. The proposed approach generally leads to 1) lower biases in flux
recovery, 2) an improved root mean-square error of up to 35% and 3) more
robustness to background fluctuations at the scale of the source. The WMAP
9-year point-source-subtracted maps are available online.
