An inverse method for in-situ estimation of acoustic surface impedance targeting inverse sounr rendering in rooms

We propose two methods based on the inverse boundary element method (IBEM) for the estimation of acoustic impedances of the interior surfaces of a room. The algorithms take as input the geometrical model of the space, a set of sound field pressures measured at random points and the vibration strength of the sound source. A first approach is a constrained leastsquares method that attempts to find simultaneously surface sound pressures and particle velocities, parameters that define the acoustic impedance. This is in contrast with previous work on similar acoustic inverse problems that solve for one parameter (typically the strength of the vibration velocity) and use regularization techniques to reduce the effects of the illconditioning and obtain smooth solutions. Our second approach is an iterative optimization process that estimates directly the sought impedances assuming that the interior surfaces have homogeneous impedance values. This assumption allows in addition a significant reduction of the dimensionality of the optimization problem. A numerical example of the performance of both methods is presented. Preliminary experiments in a reverberation chamber are also shown.