Near-field acoustic holography with iteratively reweighted least squares-based outlier rejection and TV+ℓ1 regularization.

Near-field acoustic holography (NAH) reconstructs complex acoustic pressure fields from near-field microphone measurements. The equivalent source method (ESM), which relies on least squares inversion, is highly susceptible to measurement outliers. To address this, we present an ESM-NAH reconstruction approach, iteratively reweighted least squares (IRLS)-total variation (TV) and ℓ1 regularization (IRLS-TV+ℓ1), which employs bounded-influence M-estimation with IRLS to mitigate the impact of outlier-contaminated measurements. In addition, the method incorporates TV and ℓ1 regularization to capture both extended and compact source features. To evaluate performance, we simulate a piecewise-constant block source on a 16 × 16 grid at 25 dB signal-to-noise ratio (SNR), with 5% of channels corrupted by outliers. The proposed method achieves a reconstruction relative error of 4.4% under outlier contamination, compared to 4.3% for uncorrupted data. By comparison, Tikhonov regularization degrades from 15.9% to 96.3% relative error, sparse Bayesian learning (SBL) from 26.1% to 195% relative error, and the fused total generalized variation (F-TGV) benchmark from 7.8% to 168% relative error. Experimental measurements further indicate degradation factors of 11.5×, 14.0×, and 15.9× for Tikhonov, SBL, and F-TGV, respectively, under 5% introduced outlier contamination, whereas IRLS-TV+ℓ1 exhibits only a 1.02× increase.