Source localization and signal reconstruction in a reverberant field using the FDTD method

Numerical methods applied to room acoustics are usually employed to predict the sound pressure at certain positions generated by a known source. In this paper the inverse problem is studied: given a number of microphones placed in a room, the sound pressure is known at these positions and this information may be used to perform a localization and signal reconstruction of the sound source. The source is assumed to be spatially sparse meaning it can be modeled as a point source. The finite difference time domain method is used to model the acoustics of a simple two dimensional square room and its matrix formulation is presented. A two step method is proposed. First a convex optimization problem is solved to localize the source while exploiting its spatial sparsity. Once its position is known the source signal can be reconstructed by solving an overdetermined system of linear equations.