Detailed graphical models for source separation and missing data interpolation in audio
Methods for blind source separation based only on general properties such as source independence encounter difficulties when the degree of overlap and/or the dimensionality of the observations make the blind inference problem unresolvable. Such situations require additional constraints on the form of the individual sources, motivating the development of models able to capture in detail the consistency and variability of a single source’s sound. With single-chain HMMs this requires a very large number of states, making the models marginally practical. Here we present two approaches to factorize the variability in detailed models. First is a coupled subband model, where each source signal is broken into multiple frequency bands, and separate but coupled HMMs are built for each band requiring many fewer states per model. In order to avoid the unnatural state combinations that would arise from independent models for each band (as in the multiband speech models of [1] and [2]), we couple adjacent bands resulting in a grid-like model (fig. 1) for the full spectrum. Exact inference of such a model is intractable, but we have derived an efficient approximation based on variational methods.