NON-NEGATIVE DYNAMICAL SYSTEMWITH APPLICATION TO SPEECH AND AUDIO

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 applica-tion 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 ma-trix factorization (NMF) to support Markovian dynamics. Learning and inference algorithms were derived and experiments on speech enhancement were conducted by training sparse non-negative dy-namical 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. 1