On the v-line radon transform and its imaging applications.

Area of Science:

• Medical Imaging
• Tomography
• Applied Mathematics

Background:

• Classical Radon transforms are vital for medical imaging (CT, PET).
• Existing methods struggle with scattered radiation data.
• Discontinuous curves present unique mathematical challenges.

Purpose of the Study:

• To introduce and analyze a V-line Radon transform for scattered radiation imaging.
• To develop an analytical inverse formula and reconstruction algorithm for this transform.
• To enable 2D image reconstruction from 1D scattered radiation measurements.

Main Methods:

• Definition of a Radon transform on a V-shaped discontinuous curve.
• Derivation of an analytic inverse formula for the V-line Radon transform.
• Development of a filtered back projection algorithm tailored for V-line data.

Main Results:

• The V-line Radon transform is established as fundamental for 2D scattered radiation imaging.
• An explicit inverse formula and reconstruction procedure are successfully derived.
• Numerical simulations demonstrate the feasibility of image reconstruction.

Conclusions:

• The V-line Radon transform offers a new mathematical framework for scattered radiation imaging.
• This work paves the way for advanced imaging techniques using Compton scattered radiation.
• The developed methods have potential applications in medical diagnostics and security screening.