Mapping uncertainties involved in sound source reconstruction with a cross-spectral-matrix-based Gibbs sampler

Area of Science:

• Acoustics
• Signal Processing
• Computational Mathematics

Background:

• Inverse methods for sound source reconstruction are susceptible to errors from noise and model imperfections.
• Accurate mapping of these estimation errors is crucial for reliable acoustic source localization.

Purpose of the Study:

• To develop a robust method for mapping sound source estimation errors alongside reconstructed sources.
• To provide a computationally efficient and flexible Bayesian approach for acoustic inverse problems.

Main Methods:

• Utilizing a Bayesian perspective, initializing a Gibbs sampler with the Bayesian focusing method.
• Directly operating on the cross-spectral matrix and accommodating sparse priors.
• Incorporating uncertainties in microphone positions for enhanced regularization.

Main Results:

• The proposed Gibbs sampler demonstrates rapid convergence within a few iterations, ensuring practical applicability.
• The method proves flexible across various acoustic scenarios and prior assumptions.
• Accounting for microphone position uncertainties further stabilizes the inverse problem solution.

Conclusions:

• The developed Bayesian approach effectively maps estimation errors in sound source reconstruction.
• The method offers a practical, flexible, and robust solution for complex acoustic inverse problems.
• This work enhances the reliability and accuracy of sound source localization techniques.