Christian Hansen : October 14, 2003

Inverse acoustic problems: sound source reconstruction.

Abstract

The goal of this project is to reconstruct vibration patterns on a 3D surface from measurements of the acoustic field (the pressure) at some distance. Mathematically speaking, the relation between the surface velocities and the measured pressure leads to an inverse problem that is very sensitive to data errors, and regularization is necessary in order to stabilise the solution.

In the talk we describe the problem and demonstrate how we treat it numerically by means of Tikhonov regularization combined with the L-curve criterion for choosing the regularization parameter. We also show reconstructions from real measurements, and we point to interesting numerical problems in connection with the reconstruction algorithms.

This is joint work with Brüel and Kjær, a Danish company specializing in sound and vibration measurements. More information can be found at

http://www.imm.dtu.dk/~pch/Projekter/acoustic.html