Diffusion Equation-Assisted Markov Chain Monte Carlo Methods for the Inverse Radiative Transfer Equation

Area of Science:

• Biomedical optics
• Computational imaging
• Inverse problems

Background:

• Optical tomography reconstructs tissue optical properties using light measurements.
• The radiative transfer equation (RTE) models light propagation, with inverse problems focusing on scattering coefficient reconstruction.
• In strong scattering, RTE simplifies to the diffusion equation (DE), making the inverse problem reconstructing the diffusion coefficient.

Purpose of the Study:

• To develop a computationally feasible method for sampling the posterior distribution of the scattering coefficient in optical tomography.
• To address the computational expense of traditional Markov Chain Monte Carlo (MCMC) methods for RTE-based inverse problems.

Main Methods:

• Bayesian framework for analyzing the posterior distribution of the scattering coefficient.
• Proposed a novel DE-assisted two-level MCMC technique.
• Utilized cheaper DE solvers to filter out unsuitable samples before employing expensive RTE solvers.

Main Results:

• The DE-assisted MCMC method significantly reduces the computational cost of sampling from the RTE posterior distribution.
• Demonstrated the feasibility of obtaining accurate scattering coefficient reconstructions.
• Enabled practical application of Bayesian inference in optical tomography.

Conclusions:

• The DE-assisted two-level MCMC technique provides a computationally efficient solution for optical tomography inverse problems.
• This method facilitates the application of Bayesian inference for reconstructing optical properties of biological tissues.
• Advances in computational methods are crucial for the practical implementation of advanced imaging techniques.