Filtered Backprojection Algorithms for Attenuated Parallel and Cone-Beam Projections Sampled on a Sphere

Cone-beam tomography is used in single photon emission computed tomography (SPECT) to improve the sensitivity for imaging small organs like the brain with large field-of-view gamma cameras. However, the compensation for photon attenuation is a major challenge to quantitatively reconstruct cone-beam projections or projections sampled from any imaging geometry. In SPECT imaging of the brain, fairly accurate quantitative results have been obtained for 2D parallel-beam geometry by assuming a constant attenuator. In this paper we extend these results to derive filtered backprojection (FBP) reconstruction algorithms for 3D exponential parallelbeam projections and for 3D exponential cone-beam projections with sampling on a sphere.