An Analytical Algorithm for Tensor Tomography From Projections Acquired About Three Axes

Area of Science:

• Medical Imaging
• Biophysics
• Computational Science

Background:

• Tensor fields are crucial for modeling biological tissue structures.
• Efficient tensor field measurement requires minimal projections for medical imaging.

Purpose of the Study:

• To develop a filtered back-projection algorithm for symmetric second-rank tensor field reconstruction.
• To reconstruct tensor fields using directional X-ray projections from three axes.

Main Methods:

• Decomposition of tensor fields into solenoidal and irrotational components.
• Application of the Fourier projection theorem for algorithm derivation.
• Simulation using phantoms and cardiac diffusion MRI data.

Main Results:

• Successful reconstruction of tensor fields from limited projections.
• Validation of mathematical derivations through simulations.
• Demonstration of reasonable noise properties for the algorithm.

Conclusions:

• The developed algorithm enables efficient tensor field reconstruction from X-ray projections.
• Tensor field decomposition offers insights for optimizing projection acquisition strategies.
• This work advances tensor field analysis in medical imaging.