Shifted 2D Non-negative Tensor Factorisation

Recently, non-negative matrix factor 2D deconvolution was developed as a means of separating harmonic instruments from single channel mixtures. This technique uses a model which is convolutive in both time and frequency, and so can capture instruments which have both time-varying spectra and time-varying fundamental frequencies simultaneously. However, in many cases two or more channels are available, in which case it would be advantageous to have a multi-channel version of the algorithm. To this end, a shifted 2D non-negative tensor factorisation algorithm is derived, which extends non-negative matrix factor 2D deconvolution to the multi-channel case. The use of this algorithm for multi-channel sound source separation of pitched instruments is demonstrated