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 vie wpoint of the ill-posed problem theory. The proposed approach, which permit s overcoming the difficulties related to ambiguity and instability, is base d on the variational regularization with constraints, The work of articulat ors 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 numeri cal implementation of the proposed approach is based on a local piecewise l inear approximation of the articulatory-to-acoustics mapping and a polynomi al approximation of the discrepancy measure, A heuristic method named the " calibrating curves method" is applied for estimating the accuracy of the ob tained approximate solution. It was shown that in some cases the error of t he inverse problem solution is weakly dependent on the errors of formant fr equency measurements. The vocal tract shapes obtained by virtue of the prop osed approach are very close to those measured in X-ray experiments. (C) 20 00 Elsevier Science B.V. All rights reserved.