Introduction

Sound source separation refers to the problem of synthesizing $N$ source signals given an $M$ channel mixture of those source signals. When there are fewer input mixtures than sources to be separated ($M < N$), we have the degenerate case. A special degenerate case occurs when there is only one mixture ($M = 1$). In the non-degenerate case ($M\geq N$), the basic problem is to estimate the mixing matrix to determine how the sources are combined into mixtures. This matrix may then then be inverted to obtain the input sources. In the degenerate case, it is necessary to use prior information about the source signals to perform demixing, because of the ill-posed nature of the inverse mathematical problem. In the special case of only one mixture, it is impossible to exploit any information about differences between various mixtures, and thus only information about the source signals may be used. In digital audio, the case most frequently encountered is the two mixture degenerate case, as many or most currently available commercial digital recordings contain two channels (stereo) but more than two instruments, voices, or other sounds. A variety of approaches to this and other degenerate problems have been tried. Each method exploits one or more features of the sound sources, as they must do in order to be successful. Such features include the sources' time-frequency sparsity, their time-frequency independence, and their distinct amplitude and delay characteristics between the mixtures. A brief review of these techniques is included in [1]. We find that the DUET system [2,3,1] has achieved particularly convincing results, but can still be improved. We include a brief overview of the system in section 2, and highlight a significant weakness remedied by the currently proposed system. In section 3, we explain the delay and scale subtraction scoring (DASSS) technique, that largely solves the problem. In section 5 we consider extensions of DASS that relax the initial assumptions of the DUET system.