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This paper discusses the localization of music instruments in the stereo space. The signal, composed of two channels, is decomposed into a linear combination of Stereo Instrument-Specific Harmonic atoms, that model the harmonic structure of instrument notes as a whole and whose individual angles give clues about the real angle of the sources. To get such decompositions, a Stereo Matching Pursuit algorithm has been implemented, with a phase adaptation for each signal channel. This decomposition gives neat source localizations for instantaneous mixes, and the extension to realistic convolutive mixes seems possible with adequate post-processing.