Gaussian processes for sound field reconstruction.

Area of Science:

• Acoustics
• Machine Learning
• Signal Processing

Background:

• Sound field reconstruction is crucial for acoustic analysis.
• Classical methods often rely on linear regression with limitations.
• Gaussian processes offer a probabilistic approach to spatial data modeling.

Purpose of the Study:

• To investigate Gaussian process (GP) regression for sound field reconstruction.
• To compare GP-based methods with classical linear regression techniques.
• To analyze the impact of different kernels and hierarchical Bayesian parameterization.

Main Methods:

• Utilizing Gaussian process regression with covariance functions (kernels) for spatial correlation modeling.
• Examining the relationship between GP regression and linear regression from an acoustical viewpoint.
• Introducing and analyzing a hierarchical Bayesian parameterization for a variable sparsity plane wave kernel.

Main Results:

• Gaussian processes enable sound field reconstruction from sparse observations.
• The GP approach allows for closed-form uncertainty quantification.
• A hierarchical Bayesian parameterization demonstrated superior performance across diverse sound fields.

Conclusions:

• Gaussian process regression is a powerful tool for sound field analysis.
• The hierarchical parameterization is particularly effective when prior information is unavailable.
• GP regression offers significant advantages over traditional linear regression methods for sound field reconstruction.