Non-negative data arise in a variety of important signal processing domains, such as power spectra of signals, pixels in images, and count data. This paper introduces a novel non-negative dynamical system (NDS) for sequences of such data, and describes its application to modeling speech and audio power spectra. The NDS model can be interpreted both as an adaptation of linear dynamical systems (LDS) to non-negative data, and as an extension of non-negative matrix factorization (NMF) to support Markovian dynamics. Learning and inference algorithms were derived and experiments on speech enhancement were conducted by training sparse non-negative dynamical systems on speech data and adapting a noise model to the unknown noise condition. Results show that the model can capture the dynamics of speech in a useful way.
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. ABSTRACT Non-negative data arise in a variety of important signal processing domains, such as power spectra of signals, pixels in images, and count data. This paper introduces a novel non-negative dynamical system (NDS) for sequences of such data, and describes its application to modeling speech and audio power spectra. The NDS model can be interpreted both as an adaptation of linear dynamical systems (LDS) to non-negative data, and as an extension of non-negative matrix factorization (NMF) to support Markovian dynamics. Learning and inference algorithms were derived and experiments on speech enhancement were conducted by training sparse non-negative dynamical systems on speech data and adapting a noise model to the unknown noise condition. Results show that the model can capture the dynamics of speech in a useful way.Index Terms-non-negative dynamical system (NDS), linear dynamical system (LDS), multiplicative innovations, non-negative matrix factorization (NMF), source separation.