Shifted 2D non-negative tensor factorisation

2006

Recently, shifted Non-negative Matrix Factorisation was developed as a means of separating harmonic instruments from single channel mixtures. However, in many cases two or more channels are available, in which case it would be advantageous to have a multichannel version of the algorithm. To this end, a shifted Non-negative Tensor Factorisation algorithm is derived, which extends shifted Non-negative Matrix Factorisation to the multi-channel case. The use of this algorithm for multi-channel sound source separation of harmonic instruments is demonstrated. Further, it is shown that the algorithm can be used to perform Non-negative Tensor Deconvolution, a multi-channel version of Non-negative Matrix Deconvolution, to separate sound sources which have time evolving spectra from multi-channel signals.

Computational Intelligence and Neuroscience, 2008

Recently, shift-invariant tensor factorisation algorithms have been proposed for the purposes of sound source separation of pitched musical instruments. However, in practice, existing algorithms require the use of log-frequency spectrograms to allow shift invariance in frequency which causes problems when attempting to resynthesise the separated sources. Further, it is difficult to impose harmonicity constraints on the recovered basis functions. This paper proposes a new additive synthesis-based approach which allows the use of linear-frequency spectrograms as well as imposing strict harmonic constraints, resulting in an improved model. Further, these additional constraints allow the addition of a source filter model to the factorisation framework, and an extended model which is capable of separating mixtures of pitched and percussive instruments simultaneously.

2005

An algorithm for Non-negative Tensor Factorisation is introduced which extends current matrix factorisation techniques to deal with tensors. The effectiveness of the algorithm is then demonstrated through tests on synthetic data. The algorithm is then employed as a means of performing sound source separation on two channel mixtures, and the separation capabilities of the algorithm demonstrated on a two channel mixture containing saxophone, strings and bass guitar.

2009

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 sourcefilter 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.

2007

… on Music and Machine Learning, …, 2008

A shift-invariant non-negative tensor factorisation algorithm for musical source separation is proposed which generalises previous work by allowing each source to have its own parameters rather a fixed set of parameters for all sources. This allows independent control of the number of allowable notes, number of harmonics and shifts in time for each source. This increased flexibility allows the incorporation of further information about the sources and results in improved separation and resynthesis of the separated sources.

PAMM, 2007

Providing prior knowledge about sources to guide source separation is known to be useful in many audio applications. In this paper we present two tensor factorization models for musical source separation where musical information is incorporated by using the Generalized Coupled Tensor Factorization (GCTF) framework. The approach is an extension of Nonnegative Matrix Factorization where more than one matrix or tensor object is simultaneously factorized. The first model uses a temporally aligned transcription of the mixture and incorporates spectral knowledge via coupling. In contrast of using a temporally aligned transcription, the second model incorporates harmonic information by taking an approximate, incomplete, and not necessarily aligned transcription of the musical piece as input. We evaluate our models on piano and cello duets where the experiments show that instead of using a temporally aligned transcription, we can achieve competitive results by using only a partial and incomplete transcription.

2005

2011

Non-negative Matrix Factorisation (NMF) based algorithms have found application in monaural audio source separation due to their ability to factorize audio spectrogram into additive part-based basis functions, which typically corresponds to individual notes or chords in music. These separated basis functions are usually greater in number than the active sources, hence clustering is needed for individual source signal synthesis. Although, many attempts have been made to improve the clustering of the basis functions to sources, much research is still required in this area. Recently, Shifted NMF based methods have been proposed as a means to avoid clustering these pitched basis functions to sources. However, the Shifted NMF algorithm uses a log-frequency spectrogram with a fixed number of frequency bins per octave which compromises the quality of separated sources.We show that by replacing the method used to calculate the log-frequency spectrogram with a recently proposed invertible Constant Q Transform (CQT), we can considerably improve the separation quality of the individual sound signals.