Direct integration of the inverse Radon equation for X-ray computed tomography

Area of Science:

• Medical Imaging
• Applied Mathematics
• Computer Vision

Background:

• X-ray tomography is crucial for medical imaging and non-destructive testing.
• Standard reconstruction algorithms often rely on Fourier transforms, which can be computationally intensive and sensitive to noise.
• Limited projection data poses a significant challenge in achieving accurate tomographic reconstructions.

Purpose of the Study:

• To formulate a new mathematical approach for image restoration in two-dimensional X-ray tomography.
• To develop a practical computing algorithm for X-ray tomographic reconstruction without using Fourier transformation.
• To evaluate the performance of the new approach compared to standard algorithms, particularly under conditions of limited data.

Main Methods:

• The study introduces a novel mathematical formulation based on the inverse Radon equation.
• This approach bypasses the need for Fourier transformation in the image reconstruction process.
• Software implementation was used to test and validate the proposed algorithms.

Main Results:

• The developed approach provides a more reliable mathematical foundation for tomographic reconstruction.
• Software implementation demonstrated the practical viability of the new algorithms.
• The new method significantly outperforms standard X-ray tomographic reconstruction algorithms when dealing with a low number of projections.

Conclusions:

• The proposed inverse Radon equation-based method offers a robust alternative for X-ray tomography image restoration.
• Eliminating Fourier transformation enhances mathematical reliability and computational practicality.
• This approach shows particular promise for applications with limited projection data, improving diagnostic accuracy and efficiency.