Linsen Huang

Accurate sound source localization at medium and low frequencies remains challenging due to limited spatial resolution and strong noise interference. Conventional ℓ ₁ -norm-based sparse reconstruction methods are sensitive to measurement noise and tend to underestimate strong source amplitudes. This paper proposes a novel ℓ ₁ –Cauchy hybrid regularization framework for sound field reconstruction. The ℓ ₁ norm enforces global spatial sparsity, while the Cauchy penalty mitigates amplitude bias through its heavy-tailed prior, enabling a synergistic balance between high resolution and reconstruction robustness. Numerical simulations and Monte Carlo analyses demonstrate that the proposed method achieves superior reconstruction accuracy in the medium- and low-frequency range, with enhanced robustness to variations in measurement distance and signal-to-noise ratio. Quantitative comparisons confirm that the ℓ ₁ –Cauchy approach outperforms Tikhonov regularization, wideband acoustic holography (WBH), and fast iterative Cauchy thresholding (FICTA), demonstrating its potential for practical noise source identification.

This study examines the performance of six different two-dimensional, 18-element microphone array geometries—BK, Ring, Reuleaux, Logarithmic, Triangle, and Starfish—for sound source localization. The arrays’ performances are systematically evaluated using beamforming algorithms and acoustic pressure reconstruction, focusing on key metrics such as main lobe width, side lobe magnitude, reconstruction error, and resolution quality over frequencies ranging from 0 to 3000 Hz. Additionally, the study investigates the adaptability of these configurations at various distances and explores their frequency-dependent behavior. The results indicate that array geometry substantially impacts localization accuracy, with the Starfish configuration demonstrating superior overall performance, exhibiting the narrowest main lobe width, highest main lobe amplitude, lowest reconstruction error, and consistently high resolution. Thus, the Starfish configuration is recommended as optimal for effective sound source localization applications.

Accurate sound field reconstruction, especially in medium and low-frequency ranges, remains challenging due to limitations in traditional methods relying on the ℓ ₁ norm for sparsity promotion. These approaches are vulnerable to noise interference and may underestimate high-amplitude components, affecting reconstruction stability. In this work, we propose a novel sound field reconstruction method utilizing the error function (ERF) as a surrogate for the ℓ ₀ norm to improve both the speed and robustness of reconstruction. Comparative analysis with traditional methods, including the Tikhonov regularization method, Monotonic Two-Step Iterative Shrinkage/Thresholding method (MTwIST), and ℓ ₁ -CVX, demonstrates the superior performance of the ERF method in terms of sound pressure accuracy and reconstruction reliability. Monte Carlo simulations, Receiver Operating Characteristic (ROC) analysis, and experimental results further validate that the ERF method achieves improved localization and sound field reconstruction in the low-frequency domain, with better flexibility concerning measurement distance and signal-to-noise ratio.