Multichannel High-Resolution NMF for Modeling Convolutive Mixtures of Non-Stationary Signals in the Time-Frequency Domain

• Published in: IEEE/ACM transactions on audio, speech, and language processing Vol. 22; no. 11; pp. 1670 - 1680
• Main Authors: Badeau, Roland, Plumbley, Mark D.
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.11.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Convolution; Equations; Hafnium; Mathematical model; Multichannel signal analysis; non-stationary signal modeling; nonnegative matrix factorization; Speech; Time-domain analysis; Time-frequency analysis; variational EM algorithm
• ISSN: 2329-9290; 2329-9304
• DOI: 10.1109/TASLP.2014.2341920

Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies.