Reconstructing individualized near-field head-related transfer functions from a small set of far-field data based on tensor decomposition.

Head-related transfer functions (HRTFs) are pivotal in virtual auditory displays. Near-field HRTFs generally vary with source direction, distance, frequency, and individual. This multifaceted dependence presents significant challenges in near-field HRTF measurement and calculation. This study aims to reconstruct individualized near-field HRTFs with high-directional resolution from a small set of directionally measured or calculated data at a fixed far-field distance. By using the 4th-order tensor decomposition, near-field HRTFs are decomposed into a weighted combination of direction, distance, frequency, and a small number of individual-related modes. A training dataset of near-field HRTFs is used for the decomposition to calculate universal direction-, distance-, and frequency-related modes and the weights. For new individuals excluded from this dataset, individual-related modes are estimated from a small set of directional measurements or calculations of far-field HRTFs. Subsequently, this enables the estimation of individualized near-field HRTFs with high-directional resolution. Analytical examples demonstrate that a small number (15 or 14) of individual-related modes account for over 98% of the individual-related variation in HRTF magnitude square. Furthermore, high-directional resolution near-field HRTF magnitudes can be estimated using far-field data composed of 30 or 32 directional calculations or measurements. These findings are validated through psychoacoustic experiments, confirming the efficiency of the proposed method.