The DUET and DESPRIT blind source separation algorithms attempt to recover J sources from I mixtures of these sources, in the interesting case where J > I, with minimal information about the mixing environment or underlying source statistics. We present a semi-blind generalization of the DUET-DESPRIT approach which allows arbitrary placement of the sensors and demixes the sources given the room impulse response. We learn a sparse representation of the mixtures on an over-complete spatial signatures dictionary. We localise and separate the constituent sources via binary masking of a power weighted histogram in location space or in attenuation-delay space. We demonstrate the robustness of this technique using synthetic room experiments.