Sparsity based inhomogeneous sound field estimation using multiple source-regions kernel

We propose a method for estimating an inhomogeneous sound field from microphone array signals based on the sparsity of the source distribution. Our approach begins by defining a kernel function as a weighted combination of sub-kernels, each representing spatial correlations within a specific spherical source region. A gradient-based algorithm is developed to update the kernel weights by exploiting the sparsity. Furthermore, we propose a scheme to update the kernel parameters, specifically the radii and centers of the source regions where analytical expressions for the gradients required to update both the weights and the kernel parameters are derived. A theoretical analysis reveals the relationship between the proposed method and conventional sparse point-source decomposition methods that approximate the sound field as a superposition of point sources. Numerical simulations demonstrate that the proposed method provides improved estimation accuracy compared to conventional methods.