Kernel Learning for Sound Field Estimation with L1 and L2 Regularizations

A method to estimate an acoustic field from discrete microphone measurements is proposed. A kernel-interpolation-based method using the kernel function formulated for sound field interpolation has been used in various applications. The kernel function with directional weighting makes it possible to incorporate prior information on source directions to improve estimation accuracy. However, in prior studies, parameters for directional weighting have been empirically determined. We propose a method to optimize these parameters using observation values, which is particularly useful when prior information on source directions is uncertain. The proposed algorithm is based on discretization of the parameters and representation of the kernel function as a weighted sum of sub-kernels. Two types of regularization for the weights, L1 and L2, are investigated. Experimental results indicate that the proposed method achieves higher estimation accuracy than the method without kernel learning.