Underdetermined reverberant acoustic source separation using weighted full-rank nonnegative tensor models.In this paper, a fusion of K models of full-rank weighted nonnegative tensor factor two-dimensional deconvolution (K-wNTF2D) is proposed to separate the acoustic sources that have been mixed in an underdetermined reverberant environment.  The derivation of the algorithm and the development of proposed full-rank K-wNTF2D will be shown.  The algorithm also encodes a set of variable sparsity parameters derived from Gibbs distribution into the K-wNTF2D model.  This optimizes each sub-model in K-wNTF2D with the required sparsity to model the time-varying variances of the sources in the spectrogram.  In addition, an initialization method is proposed to initialize the parameters in the K-wNTF2D. 
K-wNTF2D
The model is adapted in an unsupervised manner under the hybrid framework of the generalized expectation maximization and multiplicative update algorithms. 
the generalized expectation maximization and multiplicative update algorithms