Kernel Interpolation of Incident Sound Field in Region Including Scattering Objects

A method for estimating the incident sound field inside a region containing scattering objects is proposed. The sound field estimation method has various applications, such as spatial audio capturing and spatial active noise control; however, most existing methods do not take into account the presence of scatterers within the target estimation region. Although several techniques exist that employ knowledge or measurements of the properties of the scattering objects, it is usually difficult to obtain them precisely in advance, and their properties may change during the estimation process. Our proposed method is based on the kernel ridge regression of the incident field, with a separation from the scattering field represented by a spherical wave function expansion, thus eliminating the need for prior modeling or measurements of the scatterers. Moreover, we introduce a weighting matrix to induce smoothness of the scattering field in the angular direction, which alleviates the effect of the truncation order of the expansion coefficients on the estimation accuracy. Experimental results indicate that the proposed method achieves a higher level of estimation accuracy than the kernel ridge regression without separation.