Sparse Head-Related Impulse Response for Efficient Direct Convolution
This work addresses computational efficiency in spatial audio synthesis, which is incremental as it builds on existing HRIR methods with a novel factorization approach.
The paper tackled the problem of efficiently computing head-related impulse responses (HRIRs) for spatial audio synthesis by proposing a structural factorization into non-negative and Toeplitz matrices, resulting in a method that reduces computational cost compared to frequency-domain convolution.
Head-related impulse responses (HRIRs) are subject-dependent and direction-dependent filters used in spatial audio synthesis. They describe the scattering response of the head, torso, and pinnae of the subject. We propose a structural factorization of the HRIRs into a product of non-negative and Toeplitz matrices; the factorization is based on a novel extension of a non-negative matrix factorization algorithm. As a result, the HRIR becomes expressible as a convolution between a direction-independent \emph{resonance} filter and a direction-dependent \emph{reflection} filter. Further, the reflection filter can be made \emph{sparse} with minimal HRIR distortion. The described factorization is shown to be applicable to the arbitrary source signal case and allows one to employ time-domain convolution at a computational cost lower than using convolution in the frequency domain.