Deconvolution for the localization of sound sources using a circular microphone array

During the last decade, the aeroacoustic community has examined various methods based on deconvolution to improve the visualization of acoustic fields scanned with planar sparse arrays of microphones. These methods assume that the beamforming map in an observation plane can be approximated by a convolution of the distribution of the actual sources and the beamformer's point-spread function, defined as the beamformer's response to a point source. By deconvolving the resulting map, the resolution is improved, and the side-lobes effect is reduced or even eliminated compared to conventional beamforming. Even though these methods were originally designed for planar sparse arrays, in the present study, they are adapted to uniform circular arrays for mapping the sound over 360°. This geometry has the advantage that the beamforming output is practically independent of the focusing direction, meaning that the beamformer's point-spread function is shift-invariant. This makes it possible to apply computationally efficient deconvolution algorithms that consist of spectral procedures in the entire region of interest, such as the deconvolution approach for the mapping of the acoustic sources 2, the Fourier-based non-negative least squares, and the Richardson-Lucy. This investigation examines the matter with computer simulations and measurements.