Application of the improved fast iterative shrinkage-thresholding algorithms in sound source localization

Abstract

For acoustic beamforming, the Fast Iterative shrinkage-thresholding algorithm (FISTA) is efficient in improving the spatial resolution and the dynamic range of conventional beamforming maps. However, there are some drawbacks inherent to FISTA. In this paper, to further improve the convergence rate, numerical stability, and computation time of FISTA, adaptive step-size FISTA (AFISTA), Greedy FISTA (GFISTA) along with compression computation grid method (CG) are applied in the solving process of deconvolution beamforming. Two incoherent sinusoid sound sources with different distances, locations and frequencies are simulated and experimented to investigate the behaviors of these new algorithms (denoted as FISTA-CG, AFISTA-CG, and GFISTA-CG). Results show that all algorithms can accurately reveal the locations and amplitudes of sound sources with little differences in the high iterations. Although AFISTA-CG consumes more time during each iteration, it achieves the fastest convergence rate among these algorithms in the low iterations, and thus visualizes the accurate locations of sound sources the most rapidly in all cases. Furthermore, both AFISTA-CG and GFISTA-CG have lower convergence errors and numerical fluctuations compared with FISTA-CG.