where C is the covariance matrix of the image vector H given by
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
where the convolution of the image vector
H
is with
B, the beam response of the instrument and frequency dependance of
H
.
is the noise vector. In this case, the best reconstructed image
vector,
, is given by
where the Wiener filter, W, is given by
and
N
is the noise covariance matrix given by
. 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]).
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The Cosmic Microwave Background
Aled W. Jones and Anthony N. Lasenby http://www.livingreviews.org/lrr-1998-11 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |