  Deriving a good model for multitalker babble noise can facilitate different
speech processing algorithms, e.g. noise reduction, to reduce the so-called
cocktail party difficulty. In the available systems, the fact that the babble
waveform is generated as a sum of N different speech waveforms is not exploited
explicitly. In this paper, first we develop a gamma hidden Markov model for
power spectra of the speech signal, and then formulate it as a sparse
nonnegative matrix factorization (NMF). Second, the sparse NMF is extended by
relaxing the sparsity constraint, and a novel model for babble noise (gamma
nonnegative HMM) is proposed in which the babble basis matrix is the same as
the speech basis matrix, and only the activation factors (weights) of the basis
vectors are different for the two signals over time. Finally, a noise reduction
algorithm is proposed using the derived speech and babble models. All of the
stationary model parameters are estimated using the expectation-maximization
(EM) algorithm, whereas the time-varying parameters, i.e. the gain parameters
of speech and babble signals, are estimated using a recursive EM algorithm. The
objective and subjective listening evaluations show that the proposed babble
model and the final noise reduction algorithm significantly outperform the
conventional methods.
