Determination of particle-size distributions from light-scattering measurement using constrained Gaussian process...

Area of Science:

• Applied Mathematics
• Optical Physics
• Data Science

Background:

• Estimating particle-size distributions from optical scattering is an ill-posed inverse problem.
• Measurement noise and limited data lead to instability in traditional methods.
• Fredholm integral equations of the first kind are often used, posing significant challenges.

Purpose of the Study:

• To develop a robust methodology for estimating particle-size distributions.
• To regularize ill-posed inverse problems using Gaussian process regression.
• To integrate physical constraints effectively into the estimation process.

Main Methods:

• Constrained Gaussian process regression applied to optical scattering data.
• Integration of normalization constraints via pseudomeasurement or Lagrange multipliers.
• Spectral expansion of the covariance kernel for computational efficiency.

Main Results:

• Accurate reconstruction of particle-size distributions demonstrated through numerical experiments.
• Numerically stable, smooth, and physically interpretable results obtained.
• Efficient low-rank representation achieved without sacrificing accuracy.

Conclusions:

• The proposed constrained Gaussian process regression framework offers a principled solution.
• Addresses challenges in inverse scattering problems and ill-posed integral equations.
• Provides a robust and computationally efficient tool for particle-size analysis.