A novel Fourier-based deconvolution algorithm with improved efficiency and convergence

Linbang Shen,Yongxiang Zhang,Zhigang Chu,Yang Yang

doi:10.1177/1461348419873471

Abstract

Various deconvolution algorithms for acoustic source are developed to improve spatial resolution and suppress sidelobe of the conventional beamforming. To improve the computational efficiency and solution convergence of deconvolution, this paper proposes a Fourier-based improved fast iterative shrinkage thresholding algorithm. Simulations and experiments show that Fourier-based improved fast iterative shrinkage thresholding algorithm can achieve excellent acoustic identification performance, with high computational efficiency and good convergence. For Fourier-based improved fast iterative shrinkage thresholding algorithm, the larger the weight coefficient, the narrower the mainlobe width, and the better the convergence, but the spurious source also increases. The recommended weight coefficient for the array described herein is 3. In addition, like other Fourier-based deconvolution algorithms, Fourier-based improved fast iterative shrinkage thresholding algorithm using irregular focus grid can obtain better acoustic source identification performance than using the conventional regular focus grid.

Highlights

Array-based beamforming has become an indispensable acoustic source identification technology in some industries such as aviation aircraft,[1,2,3,4] rail train,[5] wind turbine,[6,7,8,9] mining industry,[10] and automobile[11,12,13] over decades
The core idea of these algorithms is to obtain the real information of the acoustic source through the deconvolution operation, because the output of Conventional beamforming (CB) can be approximated as the spatial convolution of the sound source distribution and the point spread function (PSF)
The above simulations are all based on the regular focus grid as shown in Figure 2(a) whose PSF shift-variant is significant, which deteriorates the identification performance of these Fourier-based deconvolution algorithms

Summary

Introduction

Array-based beamforming has become an indispensable acoustic source identification technology in some industries such as aviation aircraft,[1,2,3,4] rail train,[5] wind turbine,[6,7,8,9] mining industry,[10] and automobile[11,12,13] over decades. Like other Fourier-based deconvolution algorithms, FFT-FISTA with irregular focus point grid can overcome the deficiency of failing to accurately identify the sound source far from the center of the calculation plane.[25] FFT-FISTA is derived from FISTA and FISTA is originally proposed to solve the linear inverse problem in image processing.[26] Bhotto et al.[27] introduced a positive definite weight matrix in the gradient function minimization of FISTA and proposed improved FISTA (IFISTA) to enhance the convergence and the image reconstruction accuracy of FISTA. Inspired by Lylloff et al.,[24] Chu et al.,[25] Beck and Teboulle,[26] and Bhotto et al.,[27] to further improve the computational efficiency and the convergence of FFT-FISTA, a Fourier-based IFISTA (FFT-IFISTA) for acoustic source identification is proposed in this paper. Results of the simulation and experiment indicate that the proposed FFT-IFISTA can acquire a better acoustic identification performance with higher calculating efficiency and better convergence than other methods such as FFT-NNLS and FFT-FISTA

Methods

Results and discussions

Experiments

Conclusions