Regularization Approaches for Synthesizing HRTF Directivity Patterns

As an alternative to traditional artificial heads, it is possible to synthesize individual head-related transfer functions (HRTFs) using a so-called virtual artificial head (VAH), consisting of a microphone array with an appropriate topology and filter coefficients optimized using a narrowband least squares cost function. The resulting spatial directivity pattern of such a VAH is known to be sensitive to small deviations of the assumed microphone characteristics, e.g., gain, phase and/or the positions of the microphones. In many beamformer design procedures, this sensitivity is reduced by imposing a white noise gain (WNG) constraint on the filter coefficients for a single desired look direction. In this paper, this constraint is shown to be inappropriate for regularizing the HRTF synthesis with multiple desired directions and three alternative different regularization approaches are proposed and evaluated. In the first approach, the measured deviations of the microphone characteristics are taken into account in the filter design. In the second approach, the filter coefficients are regularized using the mean WNG for all directions. The third approach additionally takes into account several frequency bins into both the optimization and the regularization. The different proposed regularization approaches are compared using analytic and measured transfer functions, including random deviations. Experimental results show that the approach using multiple frequency bands mimicking the spectral resolution of the human auditory system yields the best robustness among the considered regularization approaches.