Ray-driven analytical fan-beam SPECT reconstruction with nonuniform attenuation

Single-photon emission computed tomography (SPECT) is based on the measurement of radiation emitted by a radiotracer injected into the patient. Because of photoelectric absorption and Compton scatter, the photons are attenuated inside the body before arriving at the detector. A quantitative reconstruction must consider the attenuation, which is usually non-uniform. Novikov and Natterer had derived an explicit formula for nonuniformly attenuated SPECT reconstruction of parallel-hole collimators. In this paper, we extend their researches to fan-beam collimators. Because any ray in fan-beam geometry can be treated as a ray in parallel-beam geometry, we derived a ray-driven analytical fan-beam reconstruction formula with non-uniform attenuation. Its accuracy is demonstrated computer simulation experiments.