Cosmic microwave background power spectrum estimation and map reconstruction with the expectation-maximization algorithm

@article{MartnezGonzlez2003CosmicMB,
  title={Cosmic microwave background power spectrum estimation and map reconstruction with the expectation-maximization algorithm},
  author={Enrique Mart{\'i}nez-Gonz{\'a}lez and Jose M. Diego and Patricio Vielva and Joseph I. Silk},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2003},
  volume={345},
  pages={1101-1109}
}
We apply the iterative expectation-maximization algorithm (EM) to estimate the power spectrum of the cosmic microwave background (CMB) from multifrequency microwave maps. In addition, we are also able to provide a reconstruction of the CMB map. By assuming that the combined emission of the foregrounds plus the instrumental noise is Gaussian distributed in Fourier space, we have simplified the EM procedure, finding an analytical expression for the maximization step. By using the simplified… 

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