6.3 The CMB power spectrum 6 Analysis of CMB data6.1 Maximum Entropy analysis

6.2 Wiener filtering

In the absence of non-Gaussian sources it is possible to simplify the Maximum Entropy method using the quadratic approximation to the entropy (Hobson et al. [57Jump To The Next Citation Point In The Article]). This has the same affect as chosing a Gaussian prior so that Equation  16Popup Equation becomes

  equation541

where C is the covariance matrix of the image vector H given by

  equation546

The solution to the analysis with this Bayesian prior is called Wiener filtering (see, for example, [38] and [97]) and has been applied to many data sets in the past when non-Gaussianity could be ignored. The data D can be written as

  equation551

where the convolution of the image vector H is with B, the beam response of the instrument and frequency dependance of H . tex2html_wrap_inline1989 is the noise vector. In this case, the best reconstructed image vector, tex2html_wrap_inline1991, is given by

  equation555

where the Wiener filter, W, is given by

  equation559

and N is the noise covariance matrix given by tex2html_wrap_inline1997 . It is important to note that not only the CMB signal but all the foregrounds are implicitly assumed to be non-Gaussian in this method ([57] [62] and [56]).



6.3 The CMB power spectrum 6 Analysis of CMB data6.1 Maximum Entropy analysis

image The Cosmic Microwave Background
Aled W. Jones and Anthony N. Lasenby
http://www.livingreviews.org/lrr-1998-11
© Max-Planck-Gesellschaft. ISSN 1433-8351
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