Estimation of stability and accuracy of inverse problem solution for the vocal tract
The inverse problem for the vocal tract is under consideration from the viewpoint of the ill-posed problem theory. The proposed approach, which permits overcoming the difficulties related to ambiguity and instability, is based on the variational regularization with constraints. The work of articulators is used as a functional of regularization and a criterion of optimality for finding an approximate solution. The measured acoustical parameters of the speech signal serve as external constraints while the geometry of the vocal tract, the mechanics of the articulation, and the phonetic properties of the language play the role of internal constraints. An effective numerical implementation of the proposed approach is based on a local piecewise linear approximation of the articulatory-to-acoustics mapping and a polynomial approximation of the discrepancy measure. A heuristic method named the calibrating curves method is applied for estimating the accuracy of the obtained approximate solution. It was shown that in some cases the error of the inverse problem solution is weakly dependent on the errors of formant frequency measurements. The vocal tract shapes obtained by virtue of the proposed approach are very close to those measured in X-ray experiments.
inverse problem speech calibrating curves solution accuracy