New Inversion Formula for the X-ray Transform and its Application to CT reconstruction

We present an inversion formula for the X-ray transform that differs in many ways from well-known results: The formula is valid for arbitrary dimensions and provides therefore an uniform approach for fan- and cone-beam Computerized Tomography. Instead of using the formula of Grangeat for linking the X-ray transform and the Radon transform the presented formula is based on a relation between the X-ray transform and the extended Radon transform. Additionally, we don't have to deal with the derivative of the Crofton symbol which is usually a discontinuous function. Applying the new formula we achieve reconstruction algorithms of filtered backprojection and filtered layergram type. The performance of the proposed algorithms is shown using simulated data.