Sparse Head-Related Impulse Response for Efficient Direct 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 directionindependent resonance filter and a direction-dependent reflection filter. Further, the reflection filter can be made 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.