Sound field reconstruction using inverse boundary element method and sparse regularization.

Area of Science:

• Acoustics
• Computational Mechanics
• Signal Processing

Background:

• The inverse boundary element method (IBEM) is crucial for reconstructing sound fields from complex surfaces.
• Conventional IBEM with Tikhonov regularization requires numerous sampling points and fine discretization, especially at high frequencies, limiting its practical application.
• Existing methods face challenges in accuracy and computational load for arbitrarily-shaped acoustic sources.

Purpose of the Study:

• To develop a more efficient and accurate method for sound field reconstruction using IBEM.
• To reduce the number of sampling points required for accurate source velocity reconstruction.
• To enhance the performance of IBEM at high frequencies through sparse regularization.

Main Methods:

• Introduced acoustic radiation modes, derived from the resistive impedance matrix eigenvectors, as a sparse basis for source surface velocities.
• Applied sparse regularization within the IBEM framework, leveraging compressive sensing principles.
• Validated the proposed method through numerical simulations and experimental measurements.

Main Results:

• Sparse regularization in IBEM significantly improves the accuracy of reconstructing source surface velocities compared to Tikhonov regularization.
• The proposed method effectively reduces the number of required sampling points, particularly beneficial for high-frequency acoustic problems.
• Numerical and experimental results confirm the superiority and effectiveness of the sparse regularization approach.

Conclusions:

• Sparse regularization offers a superior alternative to Tikhonov regularization for IBEM-based sound field reconstruction.
• The method enhances accuracy and efficiency, making it suitable for complex acoustic scenarios and high frequencies.
• Further analysis explored the impact of sampling points and signal-to-noise ratio on reconstruction performance.