Fast deconvolution algorithms have high computational efficiency, but they often overlook spatial variations in the point spread function (PSF) and wrap-around errors, resulting in the degradation of sound source imaging performance. Accordingly, this paper proposes two improved fast deconvolution algorithms based on functional beamforming (FB). The proposed algorithms establish a linear equation involving the FB output, sound source distribution, and raised-power spatial shift-invariant PSF, specially with irregular focus grid point. Furthermore, iterative solutions are obtained based on fast Fourier transform, enhancing imaging performance while maintaining computational efficiency. Simulations and experimental results demonstrate that compared to the fast deconvolution algorithms, the proposed algorithms expand the effective imaging area to 36.3°, and the Rényi entropy is reduced by approximately 45 %, which has higher imaging spatial resolution and dynamic range. Finally, the compressed gas leakage source imaging results validate the effectiveness of the proposed algorithms, indicating that they have promising engineering application prospects.
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