  The accurate and precise removal of 21-cm foregrounds from Epoch of
Reionization redshifted 21-cm emission data is essential if we are to gain
insight into an unexplored cosmological era. We apply a non-parametric
technique, Generalized Morphological Component Analysis or GMCA, to simulated
LOFAR-EoR data and show that it has the ability to clean the foregrounds with
high accuracy. We recover the 21-cm 1D, 2D and 3D power spectra with high
accuracy across an impressive range of frequencies and scales. We show that
GMCA preserves the 21-cm phase information, especially when the smallest
spatial scale data is discarded. While it has been shown that LOFAR-EoR image
recovery is theoretically possible using image smoothing, we add that wavelet
decomposition is an efficient way of recovering 21-cm signal maps to the same
or greater order of accuracy with more flexibility. By comparing the GMCA
output residual maps (equal to the noise, 21-cm signal and any foreground
fitting errors) with the 21-cm maps at one frequency and discarding the smaller
wavelet scale information, we find a correlation coefficient of 0.689, compared
to 0.588 for the equivalently smoothed image. Considering only the central 50%
of the maps, these coefficients improve to 0.905 and 0.605 respectively and we
conclude that wavelet decomposition is a significantly more powerful method to
denoise reconstructed 21-cm maps than smoothing.
