Upper bound of errors in solving the inverse problem of identifying a voice source

The paper considers the inverse problem of finding the shape of a voice-source pulse from a specified segment of a speech signal using a special mathematical model that relates these quantities. A variational method for solving the formulated inverse problem for two new parametric classes of sources is proposed: a piecewise-linear source and an A-source. The error in the obtained approximate solutions of the inverse problem is considered, and a technique to numerically estimate this error is proposed, which is based on the theory of a posteriori estimates of the accuracy in solving ill-posed problems. A computer study of the adequacy of the proposed models of sources, and a study of the a posteriori estimates of the accuracy in solving inverse problems for such sources were performed using various types of voice signals. Numerical experiments for speech signals showed satisfactory properties of such a posteriori estimates, which represent the upper bounds of possible errors in solving the inverse problem. The estimate of the most probable error in determining the source-pulse shapes for the investigated speech material is on average ~7%. It is noted that the a posteriori accuracy estimates can be used as a criterion for the quality of determining the voice-source pulse shape in the speaker-identification problem.