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

A sound field reconstruction method for a region including sources is proposed. Under the assumption of spatial sparsity of the sources, this reconstruction problem has been solved by using sparse decomposition algorithms with the discretization of the target region. Since this discretization leads to the off-grid problem, we previously proposed a gridless sound field decomposition method based on the reciprocity gap functional in the spherical harmonic domain. Even though this method allows efficient estimation with a closed-form solution while avoiding the off-grid problem, the estimation using a single time-frequency bin can be greatly affected by measurement errors. We formulate an optimization problem using the identical structure of source locations in multiple time-frequency bins and derive an algorithm based on an annihilating filter. Numerical simulation results indicated that robustness against noise can be improved by the proposed method.