Study On Fourier-based Fast Iterative Shrinkage-thresholding Deconvolution Algorithm For Acoustic Source Identification

Microphone array based beamforming acoustic source identification has become a popular technique in the field of vehicle,aerospace and other engineering due to the advantages of simple measuring,high computational efficiency,good resolution in high frequency suitability for medium-and-long distance measurement,etc.To acquire more concise identification results,the emphasis of the research is a series of clearness beamforming algorithms,especially deconvolution algorithms.This paper mainly researches and analyzes three classical kinds of fast deconvolution algorithms for planar array acoustic source identification,and carries example test verification.First of all,based on the spherical wave assumption,the theories of cross-spectral imaging function were proposed in detail and the performance evaluation indexes were expounded briefly.The results of acoustic source recognition simulation indicate that the algorithm can identify sources effectively,but suffer from wide mainlobe,poor spatial resolution,serious sidelobe contaminations.To overcome the shortcomings,the theories and formula derivation of three kinds of deconvolution are proposed such as fast iterative shrinkage-thresholding algorithm(FISTA),and the simulation show that deconvolution has narrow mainlobe,high spatial resolution,clear sidelobe but with poor computational efficiency.Then,to increase computational efficiency,with assumptive shift invariant point spread function(PSF),accelerated based on Fast Fourier Transform,Fourier-based fast iterative shrinkage-thresholding algorithm(FFT-FISTA)are proposed.At the same time,an irregular focus point grid is introduced to improve the performance.The simulation of fast deconvolution indicate that the algorithms improve spatial resolution and reduce the area of sidelobe compared to conventional beamforming,with high computational efficiency.And FFT-FISTA is the best.In addition,an irregular focus point grid can improve the spatial shift variance of real PSF and resolution of fast deconvolution.Finally,example test is adopted to valid fast deconvolution and the conclusion is consistent with the simulation.