Exact analytic reconstruction in x-ray fluorescence CT and approximated versions

Area of Science:

• Physics
• Medical Imaging
• Materials Science

Background:

• X-ray fluorescence computed tomography (XFCT) is an emerging synchrotron-based imaging technique.
• XFCT aims to reconstruct the distribution of nonradiative elements in a sample using monochromatic X-rays.
• Accurate reconstruction methods are crucial for advancing XFCT applications.

Purpose of the Study:

• To compare La Rivière's approximated inversion method for XFCT with exact analytic formulas.
• To evaluate the performance of these methods using both real and simulated XFCT data.
• To contribute to the development of more precise XFCT reconstruction algorithms.

Main Methods:

• Implementation and comparison of La Rivière's approximated inversion method.
• Application of recently derived 'exact' analytic formulae for the generalized attenuated radon transform.
• Numerical experiments utilizing both real and simulated XFCT datasets.

Main Results:

• The study provides a comparative analysis of the approximated and exact methods.
• Numerical experiments demonstrate the practical performance of the compared reconstruction approaches.
• Findings highlight the accuracy and limitations of the approximated method relative to exact solutions.

Conclusions:

• The comparison offers insights into the validity and potential biases of the approximated inversion method.
• Results guide the selection of appropriate reconstruction algorithms for XFCT.
• This work advances the understanding and application of X-ray fluorescence computed tomography.