The Generalized Back Projection Theorem for Cone Beam Reconstruction

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Abstract
The use of cone beam scanners raises the problem of three dimensional reconstruction from divergent projections. After a survey on bidimensional analytical reconstruction methods we examine their application to the 3D problem. Finally, it is shown that the back projection theorem can be generalized to cone beam projections. This allows to state a new inversion formula suitable for both the 4 π parallel and divergent geometries. It leads to the generalization of the "rho-filtered back projection " algorithm which is outlined.

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