Inverting mappings from smooth paths through R(n) to paths through R(m): A technique applied to recovering articulation from acoustics

• Published in: Speech communication 2007-05, Vol.49 (5), p.361-383
• Main Authors: Hogden, John, Rubin, Philip, McDermott, Erik, Katagiri, Shigeru, Goldstein, Louis
• Format: Article
• Language: English
• ISSN: 0167-6393
• DOI: 10.1016/j.specom.2007.02.008

Motor theories, which postulate that speech perception is related to linguistically significant movements of the vocal tract, have guided speech perception research for nearly four decades but have had little impact on automatic speech recognition. In this paper, we describe a signal processing technique named MIMICRI that may help link motor theory with automatic speech recognition by providing a practical approach to recovering articulator positions from acoustics. MIMICRI's name reflects three important operations it can perform on time-series data: it can reduce the dimensionality of a data set (manifold inference); it can blindly invert nonlinear functions applied to the data (mapping inversion); and it can use temporal context to estimate intermediate data (contextual recovery of information). In order for MIMICRI to work, the signals to be analyzed must be functions of unobservable signals that lie on a linear subspace of the set of all unobservable signals. For example, MIMICRI will typically work if the unobservable signals are band-pass and we know the pass-band, as is the case for articulator motions. We discuss the abilities of MIMICRI as they relate to speech processing applications, particularly as they relate to inverting the mapping from speech articulator positions to acoustics. We then present a mathematical proof that explains why MIMICRI can invert nonlinear functions, which it can do even in some cases in which the mapping from the unobservable variables to the observable variables is many-to-one. Finally, we show that MIMICRI is able to infer accurately the positions of the speech articulators from speech acoustics for vowels. Five parameters estimated by MIMICRI were more linearly related to articulator positions than 128 spectral energies. [Copyright 2007 Elsevier B.V.]