Tomographic Reconstruction Using Ridge Functions

Ivan Kazantsev

University of Ghent Sint Pietersnieuwstraat 41

9000 Ghent, Belgium ivan.kazantsev@elis.rug.ac.be

Abstract - In this paper tomographic reconstruction based on the concept of ridge functions (Logan and Shepp) is considered. A reconstruction approach for the ridge functions from a finite number of arbitrary projections is suggested within the framework of parallel beam geometry. The method deals with images that can be presented as a sum of ridge functions. We derive a formula to calculate the ridge functions from the set of arbitrary projections. In the case of few projections an approach for detection of ridge functions with unknown directions is suggested. Results of numerical simulation are presented.

Keywords : ridge functions, reconstruction, tomography