Spatio-temporal sparse sound field decomposition considering acoustic source signal characteristics

Abstract

We propose a sound field decomposition method that takes into consideration spatio-temporal sparsity. It has been proved that sparse representation of a sound field is effective in reducing errors originating from spatial aliasing artifacts compared with conventional plane wave decomposition. In most current methods of sparse sound field decomposition, the spatial sparsity of the sound source distribution is only assumed. However, it is known that the temporal structure of the source signal to be decomposed can also be sparse in the time-frequency domain. We formulate an objective function for sparse sound field decomposition by using the l p,q -norm to simultaneously induce sparsity in the space and time domains. An optimization algorithm on the auxiliary function method is derived to solve it. Numerical simulations of acoustic holography indicate that the reconstruction accuracy can be improved by controlling the parameter of temporal sparsity. We also demonstrate that a statistical measure of the source signals can be used as an indicator to determine a nearly optimal parameter.