Non-negative dynamical system with 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 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.