MAP Source Separation using Belief Propagation Networks

Abstract

In this paper we continue our treatment of source separation based on dynamic sparse source signal models. Source signals are modeled in frequency domain as a product of a Bernoulli selection variable with a deterministic but unknown spectral amplitude variable. The Bernoulli variable is modeled by a first order Markov process with transition probabilities learned from a training database. We consider a scenario where the mixing parameters are estimated by calibration. We derive the MAP signal estimators and show that the optimization problem reduces to a Belief Propagation Network simulation. We also present preliminary separation performance results using TIMIT database.

Estimator for Number of Sources Using Minimum Description Length Criterion for Blind Sparse Source Mixtures

“…In the past series of papers [2][3][4][5][6][7] the authors studied (1), and several generalizations of this model in the following respects. Mixing model: each channel may have an attenuation factor (equivalently, τ l may be complex); Noise statistics: noise signals may have inter-sensor correlations; Signals: more signals may non-vanish at each time-frequency point (maximum number allowed is D − 1); more recently we have considered temporal, and time-frequency, dependencies on signal statistics.…”