Sound Field Reconstruction Using Prolate Spheroidal Wave Functions and Sparse Regularization.

Area of Science:

• Acoustics
• Signal Processing
• Computational Physics

Background:

• Near-field acoustic holography (NAH) relies on compressed sensing (CS) for sound field reconstruction with limited sampling.
• Effective NAH requires optimal spatial basis selection and robust sparse regularization.
• Reconstruction of sound fields from elongated sources presents unique challenges.

Purpose of the Study:

• To propose a novel sound field reconstruction method for elongated sound sources.
• To enhance the accuracy and efficiency of near-field acoustic holography.
• To leverage prolate spheroidal wave functions (PSWFs) and orthogonal matching pursuit (OMP) for improved performance.

Main Methods:

• The proposed method combines prolate spheroidal wave functions (PSWFs) as a sparse spatial basis with the orthogonal matching pursuit (OMP) algorithm.
• PSWFs are used to represent the radiated sound field, with sparse coefficients determined by OMP.
• OMP identifies significant components by matching residual errors within a linear subspace, employing a stopping rule to prevent errors.

Main Results:

• Numerical simulations using a line-array source model demonstrated accurate reconstruction of sound pressures with a limited number of samples.
• The method showed robustness across a wide frequency range, diverse array configurations, and varying sampling numbers.
• Experimental validation confirmed the feasibility and reliability of the proposed sound field reconstruction technique.

Conclusions:

• The combination of PSWFs and OMP offers an effective solution for near-field acoustic holography of elongated sound sources.
• The proposed method achieves high accuracy and robustness, even with sparse sampling.
• This technique provides a reliable approach for detailed sound field analysis in various acoustic scenarios.