Improved FFT-FISTA algorithm based on function beamforming and its application

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Journal of Vibration and Shock ›› 2025, Vol. 44 ›› Issue (9) : 77-87.

VIBRATION THEORY AND INTERDISCIPLINARY RESEARCH

Improved FFT-FISTA algorithm based on function beamforming and its application

ZHAO Shen1,2, SHI Shaojin1, ZHOU Chao*3, LI Wei1, ZHANG Rui1, LI Junyi1

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Abstract

The Fast Iterative Shrinkage Threshold algorithm based on Fast Fourier transform (FFT-FISTA) has high computational efficiency, as it ignores the spatial variation of the point spread function and the winding error, resulting in the loss of sound source recognition performance. The improved algorithm takes the output of function beamforming as the iterative input of FFT-FISTA algorithm, establishes a linear equation system of function beamforming, sound source distribution and rising power spatial transfer invariant point spread function, and solves it iteratively based on the fast Fourier transform under the periodic boundary condition. The calculated non-periodic function is changed into a periodic function, which solves the problem of wavenumber leakage caused by the zero-filling boundary, which can improve the accuracy of the operation and further improve the imaging performance. The main lobe of the point spread function is sharpened by exponential operation, and the applicability of the assumption of spatial transfer invariance of the point spread function is expanded. The simulation and experimental results show that, compared with the conventional FFT-FISTA algorithm, the improved algorithm can improve the spatial resolution and dynamic range of the imaging, and expand the effective imaging area of the FFT-FISTA algorithm, and the experimental results of compressed gas leakage verify the effectiveness of the improved algorithm.

Key words

spread function / functional beamforming / periodic boundaries / fast Fourier transform / fast iterate on shrinking thresholds

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ZHAO Shen1, 2, SHI Shaojin1, ZHOU Chao3, LI Wei1, ZHANG Rui1, LI Junyi1. Improved FFT-FISTA algorithm based on function beamforming and its application[J]. Journal of Vibration and Shock, 2025, 44(9): 77-87

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