Bayesian Random Tomography of Particle Systems.

Area of Science:

• Imaging Science
• Computational Imaging
• Applied Mathematics

Background:

• Random tomography reconstructs 3D volumes from unknown 2D projection directions.
• This is a common challenge in various imaging applications.
• Existing methods face computational and representation limitations.

Purpose of the Study:

• To develop a novel Bayesian approach for random tomography.
• To introduce a meshless particle-based representation for 3D volumes.
• To enable efficient and accurate reconstruction from random projection data.

Main Methods:

• Utilized a mixture of spherical Gaussians as a meshless particle representation.
• Developed Markov chain Monte Carlo algorithms for inferring particle positions and orientations.
• Employed Hamiltonian Monte Carlo and a global rotational sampling strategy to address posterior sampling challenges.

Main Results:

• The particle representation allows for accelerated projection image computation.
• The method accurately and efficiently represents diverse structures.
• Successfully tested on both simulated and real-world datasets.

Conclusions:

• The proposed Bayesian approach with particle-based representation offers an effective solution for random tomography.
• Hamiltonian Monte Carlo and global rotational sampling enhance posterior inference.
• The method demonstrates robust performance in reconstructing 3D volumes from random projections.