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.

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Finding the control parameters of an articulatory model that result in given acoustics is an important problem in speech research. However, one should also be able to derive the same parameters from measured articulatory data. In this paper, a method to estimate the control parameters of the the model by Maeda from electromagnetic articulography (EMA) data, which allows the derivation of full sagittal vocal tract slices from sparse flesh-point information, is presented. First, the articulatory grid system involved in the model's definition is adapted to the speaker involved in the experiment, and EMA data are registered to it automatically. Then, articulatory variables that correspond to measurements defined by Maeda on the grid are extracted. An initial solution for the articulatory control parameters is found by a least-squares method, under constraints ensuring vocal tract shape naturalness. Dynamic smoothness of the parameter trajectories is then imposed by a variational regularization method. Generated vocal tract slices for vowels are compared with slices appearing in magnetic resonance images of the same speaker or found in the literature. Formants synthesized on the basis of these generated slices are adequately close to those tracked in real speech recorded concurrently with EMA.