Beamforming regularization matrix and inverse problems applied to sound field measurement and extrapolation using microphone array

For sound field reproduction using multichannel spatial sound systems such as Wave Field Synthesis and Ambisonics, sound field extrapolation is a useful tool for the measurement, description and characterization of a sound environment to be reproduced in a listening area. In this paper, the inverse problem theory is adapted to sound field extrapolation around a microphone array for further spatial sound and sound environment reproduction. A general review of inverse problem theory and analysis tools is given and used for the comparative evaluation of various microphone array configurations. Classical direct regularization methods such as truncated singular value decomposition and Tikhonov regularization are recalled. On the basis of the reviewed background, a new regularization method adapted to the problem at hand is introduced. This method involves the use of an a priori beamforming measurement to define a data-dependent discrete smoothing norm for the regularization of the inverse problem. This method which represents the main contribution of this paper shows promising results and opens new research avenues.