CONVEX OPTIMISATION AND SPATIAL AUDIO ANALYSES
(in collaboration with Philip Leong at the University of Sydney)
Research Team Members
Mohammad Ali Akhaee
André van Schaik
We are exploring the role of convex optimisation in spatial audio signal analyses. We have shown that the application of compressed sensing (a form of convex optimisation) can improved sound field reproduction, even when the sound field is non-sparse and reverberant. In addition, we have shown that compressed sensing can compensate for the spatial aliasing associated with spherical microphone arrays - this refers to the ability of compressed sensing to accommodate sub-Nyquist signals given appropriate sparstiy conditions. In our view, these are interesting findings. There are technical challenges in performing convex optimisation on multichannel audio signals as well as theoretical underpinnings which we are trying to better understand. In particular, we are exploring the benefits of applying our analyses in the HOA (higher-order ambisonics) or Fourier-Bessel signal domain. We are trying to integrate the convex optimisation techniques with other sound field analysis techniques such as blind source separation and source localisation. We are exploring methods to facilitate and improve the efficiency of our convex optimisation calculations using graphical processing units and/or Field-Programmable Gate Arrays.
Figure 1: We compare the sound field reconstruction results that are obtained using a Tikhonov regularised pseudo-inverse method with the compressed sensing method. In (a) the frequency is 2 kHz and spatial aliasing is not a problem; in (b) the frequency is 16 kHz and spatial aliasing now is a problem and we have sub-Nyquist spatial sampling.