  We present an application of the fast Independent Component Analysis method
to the COBE-DMR 4yr data. Although the signal-to-noise ratio in the COBE-DMR
data is typically $\sim 1$, the approach is able to extract the CMB signal with
high confidence when working at high galactic latitudes. The reconstructed CMB
map shows the expected frequency scaling of the CMB. We fit the resulting CMB
component for the rms quadrupole normalisation Qrms and primordial spectral
index n and find results in excellent agreement with those derived from the
minimum-noise combination of the 90 and 53 GHz DMR channels without galactic
emission correction. Including additional channels (priors) such as the Haslam
map of radio emission at 408 MHz and the DIRBE 140um map of galactic infra-red
emission, the FastICA algorithm is able to both detect galactic foreground
emission and separate it from the dominant CMB signal. Fitting the resulting
CMB component for Qrms and n we find good agreement with the results from
Gorski et al.(1996) in which the galactic emission has been taken into account
by subtracting that part of the DMR signal observed to be correlated with these
galactic template maps. We further investigate the ability of FastICA to
evaluate the extent of foreground contamination in the COBE-DMR data. We
include an all-sky Halpha survey (Dickinson, Davies & Davis 2003) to determine
a reliable free-free template. In particular we find that, after subtraction of
the thermal dust emission predicted by the Finkbeiner, Davis & Schlegel (1999)
model 7, this component is the dominant foreground emission at 31.5 GHz. This
indicates the presence of an anomalous dust correlated component which is well
fitted by a power law spectral shape $\nu^{-\beta}$ with $\beta \sim 2.5$ in
agreement with Banday et al. (2003).
