Region-to-Region Kernel Interpolation of Acoustic Transfer Functions Constrained by Physical Properties

A method to interpolate the acoustic transfer function (ATF) between regions using kernel ridge regression (KRR) is proposed. Conventionally, the ATF interpolation problem is strongly restricted and situational, depending on knowledge of environmental conditions while not accounting for source position variation. We derive our interpolation function as the solution of an optimization problem defined on a function space where every element holds the acoustic properties of the ATF. By making the space a reproducing kernel Hilbert space (RKHS), we can guarantee that our problem has a known and unique optimizer. The generality of the formulation of this method enables region-to-region estimations, with variable source and receiver within the assigned bounds. The definition of a RKHS also allows for the use of kernel principal component analysis, thereby efficiently providing greater noise robustness to our interpolation function. Our proposed method is compared with a previously established region-to-region interpolation method in numerical simulations where the advantages of the KRR approach are confirmed, showing lower error and greater stability for higher frequencies.