Exterior and Interior Sound Field Separation Using Convex Optimization: Comparison of Signal Models

Abstract

An exterior (direct source) and interior (reverber-ant) sound field separation method using a convex optimization algorithm is proposed. Extracting the exterior sound field from mixed observations using multiple microphones can be an effective preprocessing approach to analyzing the sound field inside a region including sources in a reverberant environment. We formulate signal models of the exterior and interior sound fields by exploiting the signal characteristics of each sound field. The interior sound field is sparsely represented using overcomplete plane- wave functions. Two models using harmonic functions and a low-rank structure are proposed for the exterior sound field. The separation algorithms for each model are derived by the alternating direction method of multipliers. Numerical simulation results indicate that higher separation accuracy than that for existing methods can be achieved by the proposed method with a small number of microphones and a flexible microphone arrangement.