Abstract : Spectral matching ICA (SMICA) is a source separation method based on covariance matching in Fourier space that was designed to address in a flexible way some of the general problems raised by Cosmic Microwave Background data analysis. However, a common issue in astronomical data analysis is that the observations are unevenly sampled or incomplete maps with missing patches or intentionally masked parts. In addition, many astrophysical emissions are not well modeled as stationary processes over the sky. These effects impair data processing techniques in the spherical harmonics representation. This paper describes a new wavelet transform for spherical maps and proposes an extension of SMICA in this space-scale representation.