论文信息 - Derivation of the Extended Fan-Beam Formula

Derivation of the Extended Fan-Beam Formula

The fan-beam tomographic reconstruction formulas that have previously appeared in the literature have been restricted to the case where the source points are situated on a circle. This paper extends the fan-beam formula to "curves of source points" other than a circle of source points (e.g., a straight line or a hexagon). In the derivation new mathematical techniques are presented. For both the straight line and the hexagon a discrete version of the "extended" formula is developed.

Bruce D. Smith

[1] G. Kowalski. Fast 3-D scanning systems using a limited tilting angle. , 1977, Applied optics.

[2] G. Herman,et al. Fast Image Reconstruction Based on a Radon Inversion Formula Appropriate for Rapidly Collected Data , 1977 .

[3] Berthold K. P. Horn. Density reconstruction using arbitrary ray-sampling schemes , 1978 .

[4] Berthold K. P. Horn. Fan-beam reconstruction methods , 1979, Proceedings of the IEEE.

[5] James G. Colsher,et al. Use of Position Sensitive Detectors in Positron Imaging , 1980, IEEE Transactions on Nuclear Science.

[6] Gabor T. Herman,et al. A Scientific Study of Filter Selection for a Fan-Beam Convolution Reconstruction Algorithm , 1980 .

[7] Bruce D. Smith. Image Reconstruction from Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods , 1985, IEEE Transactions on Medical Imaging.