Information-theoretic discrepancy based iterative reconstructions (IDIR) for polychromatic x-ray tomography | JoVE Visualize

Area of Science:

Medical Imaging
Computational Physics
Image Reconstruction

Background:

Clinical X-ray sources emit polychromatic photons with varying energies.
Existing tomographic reconstruction methods often use the monochromatic approximation, neglecting photon energy variations.
This simplification can lead to inaccuracies in reconstructed images.

Purpose of the Study:

To develop a novel family of iterative reconstruction methods that incorporate an exact polychromatic X-ray model.
To improve the accuracy and quality of tomographic image reconstruction by accounting for the full spectrum of X-ray photons.
To address the limitations of the monochromatic approximation in transmission tomography.

Main Methods:

Employed the generalized information-theoretic discrepancy (GID) as a metric for data inconsistency.
Developed a polychromatic reconstruction objective function, simplified to a paraboloidal form using surrogate functions and alternating minimization.
Derived a closed-form update formula based on the optimization transfer principle, leading to the information-theoretic discrepancy based iterative reconstructions (IDIR) algorithm.

Main Results:

The proposed IDIR framework accurately models polychromatic X-ray data without the monochromatic approximation.
IDIR variants, particularly those using log-transformed data, demonstrated superior reconstruction quality and faster convergence compared to conventional methods.
Numerical experiments showed IDIR with raw data converged faster than existing statistical reconstruction methods.

Conclusions:

The developed IDIR framework offers an effective iterative inversion of the polychromatic data model for tomographic reconstruction.
The generalized information-theoretic discrepancy (GID) provides a flexible metric for designing objective functions in iterative reconstruction.
The proposed methods outperform both monochromatic approximation-based and existing polychromatic model-based techniques, with potential applications in other challenging imaging tasks.