Gridless Sound Field Decomposition Based on Reciprocity Gap Functional in Spherical Harmonic Domain

A gridless sound field decomposition method based on the reciprocity gap functional (RGF) is proposed. An intuitive and powerful way of reconstructing a sound field inside a region including sound sources is to decompose the sound field into Green's functions. Current methods based on sparse representation require discretization of the reconstruction region into grid points to construct the dictionary matrix; however, this procedure causes an off-grid problem and has a high computational cost. We apply the RGF, which was first proposed in the field of inverse problems, to sound field decomposition in the spherical harmonic domain. The proposed method enables a sound field to be decomposed in a gridless manner with a computationally efficient algorithm. Numerical simulation results indicated that the reconstruction accuracy as well as the source localization accuracy can be improved by the proposed method compared with current methods, especially at low frequencies.