Underdetermined Audio Source Separation using Laplacian Mixture Modelling

Abstract The problem of underdetermined audio source separation has been ex-plored in the literature for many years. The instantaneous K-sensors, L-sources mixing scenario (where K < L) has been tackled by many different approaches, provided the sources remain quite distinct in the virtual positioning space spanned by the sensors. In this case, the source separation problem can be solved as a direc-tional clustering problem along the source position angles in the mixture. The use of Laplacian Mixture Models in order to cluster and thus separate sparse sources in un-derdetermined mixtures will be explained in detail in this chapter. The novel Gener-alised Directional Laplacian Density will be derived in order to address the problem of modelling multidimensional angular data. The developed scheme demonstrates robust separation performance along with low processing time.