Non-convex ℓ 1 -Cauchy hybrid penalty for sparse sound field reconstruction

Abstract 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.