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Electrical and electronic engineering
Recently, tensor decompositions have found use in sound source separation. In particular, non-negative tensor decompositions have received a lot of attention due to their ability to decompose audio spectrograms into meaningful ”parts” such as individual notes. Extensions to the basic non-negative tensor factorisation framework allow the incorporation of additional constraints, such as shift-invariance in both frequency and time. This enables the factorisations to capture more complex structures than individual notes, such as individual sources playing diﬀerent pitches and time-evolving instrument timbres. Further music speciﬁc constraints such as harmonicity and source-ﬁlter modeling have been shown to improve separation performance for musical signals. Other recent advances also allow the incorporation of Bayesian priors into these models, thereby further improving the separations obtained.
Fitzgerald, D. Musical Sound Source Separation using extended tensor decompositions, International Symposium on Nonlinear Theory and its Applications, Sapporo, Japan, 2009.