A Robust Denoised Algorithm Based on Hessian–Sparse Deconvolution for Passive Underwater Acoustic Detection

Digital beamforming techniques find wide applications in the field of underwater acoustic array signal processing. However, their azimuthal resolution has long been constrained by the Rayleigh limit, consequently limiting their detection performance. In this paper, we propose a novel two-dimensional Hessian–sparse deconvolution algorithm based on image processing techniques. This method assumes a priori that the underwater acoustic bearing time record (BTR) images exhibit sparsity, and then it first constructs partial differential equations in the beamforming domain with sparsity-norm constraints for optimal noise reduction. Subsequently, a two-dimensional deconvolution operation is applied to narrow the main lobe, aiming to achieve additional temporal gains in two-dimensional processing. The simulation and real sea trial data processing results show that the main lobe width of the proposed method is about 1.3 degrees at 0 dB. It effectively reduces the main lobe width and enhances the detection resolution of BTRs in the post-processing part, especially in low-signal-to-noise-ratio (SNR) environments. Therefore, the proposed method provides nice opportunities to further improve the target-detecting ability of hydrophone arrays.