Bayesian reconstruction of surface shape from phaseless scattered acoustic data.

Area of Science:

• Acoustics
• Materials Science
• Statistical Physics

Background:

• Reconstructing rough surface geometry from scattered waves is crucial for applications in medicine, water engineering, and structural health monitoring.
• Current methods for surface profile reconstruction lack inherent uncertainty prediction.
• Quantifying reconstruction uncertainty is essential for reliable application of these techniques.

Purpose of the Study:

• To develop a physics-informed Bayesian framework for inferring rough surface properties and their uncertainties.
• To incorporate the validity region of the Kirchhoff approximation into the Bayesian formulation.
• To assess the effectiveness of the proposed method using experimental data.

Main Methods:

• Utilized a Bayesian framework with an adaptive Metropolis scheme to infer surface properties.
• Employed the Kirchhoff approximation, constrained by surface smoothness assumptions, as the wave scattering model.
• Incorporated the validity region of the scattering model into the Bayesian inference process.
• Validated the approach on experimental data from sinusoidal and random roughness profiles.

Main Results:

• The Bayesian approach successfully recovered surface properties and provided confidence intervals, quantifying reconstruction uncertainty.
• The physics-informed method demonstrated improved performance by integrating model validity constraints.
• Experimental validation confirmed the ability of the method to identify uncertainty in surface reconstruction.

Conclusions:

• The developed Bayesian framework effectively quantifies uncertainty in rough surface reconstruction from scattered sound.
• This physics-informed approach offers a reliable method for estimating confidence intervals in surface property inference.
• The technique has potential applications in various fields requiring accurate surface characterization and uncertainty assessment.