Evaluation of the 3-D radon transform algorithm for cone beam reconstruction

Pierre P. Grangeat; Patrick Le Masson; Pierre Melennec; Pascal Sire

doi:10.1117/12.45229

1 June 1991 Evaluation of the 3-D radon transform algorithm for cone beam reconstruction

Pierre P. Grangeat, Patrick Le Masson, Pierre Melennec, Pascal Sire

Proceedings Volume 1445, Medical Imaging V: Image Processing; (1991) https://doi.org/10.1117/12.45229
Event: Medical Imaging '91, 1991, San Jose, CA, United States

Abstract

The cone beam X-ray transform modelizes the measurements on new 3D medical imaging devices using 2D detectors, for instance X-ray transmission tomographs using image intensifiers or gamma-ray emission tomographs using convergent collimators. The most commonly used reconstruction algorithm performs cone beam back projection (FELDKAMP 1984). But it induces some distortions for objects far from the plane of the cone apex. We have established an exact formula between the cone beam X-ray transform and the first derivative of the 3D Radon transform (GRANGEAT 1987). It shows that the distortions are induced by the shadow zone in the Radon domain related to the planes which intersect the object but not the apex trajectory. In the Radon domain, it becomes possible to restore the missing information by interpolation. Then the reconstruction principle is to compute and to invert the first derivative of the Radon transform. In this communication, we compare these two algorithms on reconstructions performed on simulated acquisitions. We study the shape and level distortions along lines parallel to the rotation axis. We present an analysis of the axial and radial variations of the Modulation Transfer Function (MTF) and of their distortions. We conclude that the Radon transform algorithm provides a regularized solution to the distortions, with optimized computing time on modern scientific computers.

Citation Download Citation

Pierre P. Grangeat, Patrick Le Masson, Pierre Melennec, and Pascal Sire "Evaluation of the 3-D radon transform algorithm for cone beam reconstruction", Proc. SPIE 1445, Medical Imaging V: Image Processing, (1 June 1991); https://doi.org/10.1117/12.45229

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