Deconvolution for three-dimensional acoustic source identification based on spherical harmonics beamforming. (26th May 2015) - Chu, Zhigang; Yang, Yang; He, Yansong
Abstract: Spherical Harmonics Beamforming (SHB) with solid spherical arrays has become a particularly attractive tool for doing acoustic sources identification in cabin environments. However, it presents some intrinsic limitations, specifically poor spatial resolution and severe sidelobe contaminations. This paper focuses on overcoming these limitations effectively by deconvolution. First and foremost, a new formulation is proposed, which expresses SHB's output as a convolution of the true source strength distribution and the point spread function (PSF) defined as SHB's response to a unit-strength point source. Additionally, the typical deconvolution methods initially suggested for planar arrays, deconvolution approach for the mapping of acoustic sources (DAMAS), nonnegative least-squares (NNLS), Richardson–Lucy (RL) and CLEAN, are adapted to SHB successfully, which are capable of giving rise to highly resolved and deblurred maps. Finally, the merits of the deconvolution methods are validated and the relationships of source strength and pressure contribution reconstructed by the deconvolution methods vs. focus distance are explored both with computer simulations and experimentally. Several interesting results have emerged from this study: (1) compared with SHB, DAMAS, NNLS, RL and CLEAN all can not only improve the spatial resolution dramatically but also reduce or even eliminate the sidelobes effectively, allowing clear and unambiguous identification of single source or incoherent sources. (2) The availability of RL for coherent sources is highest, then DAMAS and NNLS, and that of CLEAN is lowest due to its failure in suppressing sidelobes. (3) Whether or not the real distance from the source to the array center equals the assumed one that is referred to as focus distance, the previous two results hold. (4) The true source strength can be recovered by dividing the reconstructed one by a coefficient that is the square of the focus distance divided by the real distance from the source to the array center. (5) The reconstructed pressure contribution is almost not affected by the focus distance, always approximating to the true one. This study will be of great significance to the accurate localization and quantification of acoustic sources in cabin environments. Highlights: A new convolution formulation is proposed for Spherical Harmonics Beamforming. Deconvolution is realized to get clear maps for sources in 3D cabin environments. Availability of RL for coherent sources is highest, and that of CLEAN is lowest. Reconstructed source strength is proportional to the square of the focus distance. Reconstructed pressure contribution is almost not affected by the focus distance.