  This paper presents a prescription for distilling the information contained
in the cosmic microwave background radiation from multiple sky maps that also
contain both instrument noise and foreground contaminants. The prescription is
well-suited for cosmological parameter estimation and accounts for
uncertainties in the cosmic microwave background extraction scheme. The
technique is computationally viable at low resolution and may be considered a
natural and significant generalization of the "Internal Linear Combination"
approach to foreground removal. An important potential application is the
analysis of the multi-frequency temperature and polarization data from the
forthcoming Planck satellite.
