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A method to estimate an acoustic field from discrete microphone measurementsis proposed. A kernel-interpolation-based method using the kernel functionformulated for sound field interpolation has been used in various applications.The kernel function with directional weighting makes it possible to incorporateprior information on source directions to improve estimation accuracy. However,in prior studies, parameters for directional weighting have been empiricallydetermined. We propose a method to optimize these parameters using observationvalues, which is particularly useful when prior information on sourcedirections is uncertain. The proposed algorithm is based on discretization ofthe parameters and representation of the kernel function as a weighted sum ofsub-kernels. Two types of regularization for the weights, $L_1$ and $L_2$, areinvestigated. Experimental results indicate that the proposed method achieveshigher estimation accuracy than the method without kernel learning.

Kernel Learning For Sound Field Estimation With L1 and L2 Regularizations