A non-linear spatial hearing model based on bases pursuit algorithm

Abstract

In the research on spatial hearing and realization of virtual auditory space, it is important to effectively model the head-related transfer functions (HRTFs) or head-related impulse responses (HRIRs). In our study, we managed to carry out adaptive non-linear approximation in the field of wavelet transformation. The results show that the HRIRs  adaptive non-linear approximation model is a more effective data reduction model, is faster, and is 5 dB on average better than the traditional principal component analysis (PCA) (Karhunen-Lo?ve transform) model based on relative mean square error (MSE) criterion. Furthermore, we also discussed the best bases  choice for the time-frequency representation of HRIRs, and the results show that local cosine bases are more propitious to HRIRs  adaptive approximation than wavelet and wavelet packet base. However, the improved effect of local cosine bases is not distinct. Here, for the sake of modeling the HRIRs more truthfully, we consider choosing optimal time-frequency atoms from redundant dictionary to decompose this kind of signals of HRIRs and achieve better results than all the previous models.