Most work on foreground removal has treated the case where the frequency dependence of all components is perfectly known and independent of position .
In contrast , real-world foregrounds are generally not perfectly correlated between frequencies , with the spectral index varying slightly with position and ( in the case of some radio sources ) with time .
A method incorporating this complication in presented , and illustrated with an application to the upcoming satellite missions MAP and Planck .
We find that even spectral index variations as small as \Delta \alpha \sim 0.1 can have a substantial impact on how channels should be combined and on attainable accuracy .