A FDK-Based Reconstruction Method for Off-Centered Circular Trajectory Cone Beam Tomography

In the framework of post-genomic era, computed tomography (CT) and positron emission tomography (PET) systems were recently adapted to the new requirements of small animal imaging. In order to combine ideally anatomical and functional informations, simultaneous acquisitions of the two modalities are necessary. In this context, we studied the tomographic reconstruction required by a new prototype of PET/CT micro-system where the X-ray source has to be off-centered. In contrast to conventional micro-CT where the source and detector rotate in the same plane, our configuration imposes that the source point and its orthogonal projection on the detector plane describe two parallel distinct circles. To address this specific geometry, we derive a new general formulation of the Feldkamp (FDK) algorithm. This formula, called alpha-FDK, with alpha representing the off-center angle of the source, is evaluated using computer simulations. While the image quality obtained for small values of alpha(<17deg) is comparable to that obtained in standard circular cone beam geometry, strong artifacts appear for higher values. In order to interpret these degradations, we first analyze the projection/reconstruction system in terms of the impulse response and show the insufficiency of ramp filtering. Second, the missing data problem due to the off-centered geometry is analyzed in the Radon space