A ray-driven approach to analytical SPECT reconstruction of non-uniform attenuation with variable focal-length fan-beam collimators

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 γ photons are attenuated inside the body before arriving at the detector. A quantitative reconstruction must consider the attenuation, which is usually non-uniform. Novikov had derived an explicit formula for non-uniformly attenuated SPECT reconstruction of parallel-beam collimators. In this paper, we extend their researches to variable focal-length fan-beam collimators, and derived a ray-driven analytical variable fan-beam reconstruction formula with non-uniform attenuation. Its accuracy is demonstrated by computer simulation experiments.