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

 
: Oeckl, S.

Noo, Frederic ; University of Utah:
Third International Conference on Image Formation in X-Ray Computed Tomography 2014. Proceedings : June 22-25, 2014, Salt Lake City, Utah, USA
Salt Lake City/Utah, 2014
pp.315-318
International Conference on Image Formation in X-Ray Computed Tomography <3, 2014, Salt Lake City/Utah>
English
Conference Paper
Fraunhofer IIS ()

Abstract
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.

: http://publica.fraunhofer.de/documents/N-477034.html