Near-field acoustic holography using prolate spheroidal wave functions and Sparse Bayesian Learning

Accurate reconstruction and prediction of radiated acoustic fields from large-aspect-ratio sound sources, such as underwater vehicles and slender structures, are limited by model mismatch, dense measurement requirements, and sensitivity to measurement noise. This study develops a near-field acoustic holography method that integrates Prolate Spheroidal Wave Functions (PSWFs) with Sparse Bayesian Learning (SBL), termed PSWF-SBL. PSWFs provide a compact basis whose axial extension and energy-concentration properties are well suited to the axially extended spatial characteristics of these fields, while SBL adaptively estimates expansion coefficients, selects effective basis functions, and suppresses redundant high-order components without a prescribed sparsity level. Numerical results for a line-array monopole equivalent source model show that, under the same SBL solver, PSWFs yield lower and less frequency-sensitive reconstruction and prediction errors than cylindrical, spherical, and plane wave functions over 110–1010 Hz. With PSWF expansion, SBL also yields higher accuracy and better numerical stability than the Moore–Penrose pseudoinverse and Tikhonov regularization. Under noiseless full-measurement conditions, relative errors on all four data-acquisition surfaces remain below 1 %. At SNRs of 20 and 30 dB, errors on the reconstruction surface and two prediction surfaces remain below 3 %. Under noiseless sparse sampling, errors on all four data-acquisition surfaces remain below 5 % at a spatial sampling rate of 33.3 %. A four-loudspeaker experiment in an anechoic chamber further confirms the feasibility of PSWF-SBL under measurement and sparse-sampling conditions. PSWF-SBL therefore reduces measurement requirements while preserving reconstruction and prediction accuracy, thereby lowering array-deployment and data-acquisition costs.