Noisy cGMM: Complex Gaussian Mixture Model with Non-Sparse Noise Model for Joint Source Separation and Denoising

Here we introduce a noisy cGMM, a probabilistic model for noisy, mixed signals observed by a microphone array for joint source separation and denoising. In a conventional time-varying complex Gaussian mixture model (cGMM), the observed signals are assumed to be composed of sparse target signals only, where the sparseness refers to the property of having significant power at only a few time-frequency points. However, this assumption becomes inaccurate in the presence of non-sparse signals such as background noise, which renders speech enhancement based on the cGMM less effective. In contrast, the proposed noisy cGMM is based on the assumption that the observed signals consist of not only sparse target signals but also non-sparse background noise. This enables the noisy cGMM to model the observed signals accurately even in the presence of non-sparse background noise, which leads to effective speech enhancement. We also propose a joint diagonalization-based algorithm for estimating the model parameters of the noisy cGMM, which is significantly faster than the standard EM algorithm without any performance degradation. Indeed, the joint diagonalization bypasses the need for matrix inversion, matrix multiplication, and determinant computation at each time-frequency point, which are needed in the EM algorithm. In an experiment, the noisy cGMM outperformed the cGMM in joint source separation and denoising.