Group-Sparse Gaussian Process Regression for Inhomogeneous Sound Field Estimation

This paper proposes a kernel optimization method based on group sparsity. As a framework for inhomogeneous sound field estimation, Gaussian process regression (GPR) using a kernel function that decomposes the measured pressures into contributions from the source distributions has been investigated in prior work. While this approach demonstrated higher estimation accuracy over a wider frequency range compared to conventional methods based on the point-source decomposition, it relied on prior knowledge of the source positions. A method is proposed to optimize the weights of the kernel function directly from microphone observations, without requiring prior information on the source positions. The proposed method exploits two assumptions regarding the source distribution: (i) it is spatially sparse, and (ii) it remains identical across frequencies. Numerical simulations confirmed that the proposed method achieves higher estimation accuracy than conventional approaches.