Sparse Reconstruction of Sound Field Using Bayesian Compressive Sensing and Equivalent Source Method.

Area of Science:

• Acoustics
• Signal Processing
• Computational Physics

Background:

• Accurate sound field reconstruction is crucial for applications like acoustic imaging and noise control.
• Traditional methods often require a dense array of measurement points, limiting practical applications.
• Undersampling poses significant challenges to achieving reliable sound field reconstruction.

Purpose of the Study:

• To develop an advanced sound field reconstruction method that overcomes the limitations of sparse measurements.
• To enhance the accuracy and robustness of sound field reconstruction, particularly in low signal-to-noise ratio environments.
• To validate the proposed method's performance through numerical simulations and experimental verification.

Main Methods:

• A novel sound field reconstruction model combining the equivalent source method (ESM) with sparse Bayesian compressive sensing (BCS).
• Utilizing MacKay iteration for relevant vector machine (RVM) to infer hyperparameters and estimate sound source strength and noise variance.
• Determining optimal sparse coefficients for equivalent sound sources to achieve sparse reconstruction of the sound field.

Main Results:

• The proposed BCS-based method demonstrates significantly higher accuracy across the entire frequency range compared to the conventional ESM.
• The method exhibits superior reconstruction performance and broader frequency applicability even with undersampled measurement points.
• Demonstrated significantly lower reconstruction errors in low signal-to-noise ratio environments, indicating enhanced anti-noise capabilities and robustness.

Conclusions:

• The proposed Bayesian compressive sensing method provides a superior and reliable approach for sound field reconstruction with limited measurement points.
• The method offers improved accuracy, wider frequency applicability, and enhanced robustness against noise compared to existing techniques.
• This work contributes to advancing acoustic measurement and analysis techniques in challenging conditions.