Optimized Iterative Shrinkage Threshold Generalized Inverse Beamforming for Sound Source Localization

Abstract This work addresses underwater noise source localization. Leveraging the spatial sparsity of sound sources, we employ an optimized iterative shrinkage-thresholding generalized inverse beamforming (OISTA-GIB) method to localize noise sources. Firstly, the sparsity of sound sources is exploited by introducing the l 1 norm, resulting in an objective function that combines the l 1 norm with generalized inverse beamforming. This function is solved using an iterative shrinkage-thresholding algorithm (ISTA) to obtain sound source positions. Secondly, we note that when ISTA solves this objective function, the penalty strength applied by the identity matrix to all scanning points on the sound source surface is uniform. This uniformity reduces positioning accuracy. To enhance localization accuracy and spatial resolution, we propose an iterative regularization matrix-optimized ISTA to solve the objective function. Here, the result from the previous iteration is used to construct a regularization matrix that increases the penalty strength in non-source regions during the current iteration. This process iteratively narrows the mainlobe width in source regions until termination conditions are met, yielding refined sound source positions. Finally, simulations and experimental data processing show that the proposed OISTA-GIB method achieves higher accuracy and spatial resolution in noise source localization compared to existing methods.