Acoustic-to-articulatory inversion is a difficult problem mainly because of the nonlinearity between the articulatory and acoustic spaces and the nonuniqueness of this relationship. To resolve this problem, we have developed an inversion method that provides a complete description of the possible solutions without excessive constraints and retrieves realistic temporal dynamics of the vocal tract shapes. We present an adaptive sampling algorithm to ensure that the acoustical resolution is almost independent of the region in the articulatory space under consideration. This leads to a codebook that is organized in the form of a hierarchy of hypercubes, and ensures that, within each hypercube, the articulatory-to-acoustic mapping can be approximated by means of a linear transform. The inversion procedure retrieves articulatory vectors corresponding to acoustic entries from the hypercube codebook. A nonlinear smoothing algorithm together with a regularization technique is then used to recover the best articulatory trajectory. The inversion ensures that inverse articulatory parameters generate original formant trajectories with high precision and a realistic sequence of the vocal tract shapes.

The paper presents extensions of the single-matrix formulation (Mokhtari et al., 2008, Speech Comm. 50(3) 179-190) that enable self-oscillation models of vocal folds, including glottal chink, to be connected to the vocal tract.