Sound Field Reconstruction Using Error Function Method

The accurate sound field reconstruction, especially in medium- and low-frequency ranges, remains challenging due to limitations in traditional methods relying on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{{1}}$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{{0}}$ </tex-math></inline-formula> 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 (MTwIST) method, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{{1}}$ </tex-math></inline-formula>-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 (SNR).