Sparse Non-negative Tensor 2D Deconvolution (SNTF2D) for multi channel time-frequency analysis

We recently introduced two algorithms for sparse non-negative matrix factor 2-D deconvolution (SNMF2D) that are useful for single channel source separation and music transcription. We here extend this approach to the analysis of the log-frequency spectrograms of a multichannel recording. The model proposed forms a non-negative tensor factor 2-D deconvolution (NTF2D) based on the parallel factor (PARAFAC) model. Two algorithms are given for NTF2D; one based on least squares the other on Kullback-Leibler divergence minimization. Both algorithms are extended to give sparse decompositions. The algorithms are demonstrated to successfully identify the components of both artificially generated as well as real stereo music.