  It is a recurrent issue in astronomical data analysis that observations are
unevenly sampled or incomplete maps with missing patches or intentionaly masked
parts. In addition, many astrophysical emissions are non stationary processes
over the sky. Hence spectral estimation using standard Fourier transforms is no
longer reliable. Spectral matching ICA (SMICA) is a source separation method
based on covariance matching in Fourier space which is successfully used for
the separation of diffuse astrophysical emissions in Cosmic Microwave
Background observations. We show here that wavelets, which are standard tools
in processing non stationary data, can profitably be used to extend SMICA.
Among possible applications, it is shown that gaps in data are dealt with more
conveniently and with better results using this extension, wSMICA, in place of
the original SMICA. The performances of these two methods are compared on
simulated CMB data sets, demonstrating the advantageous use of wavelets.
