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An analytical inversion of the nonuniformly attenuated Radon transform with variable focal-length fan-beam collimators

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3 Author(s)
Junhai Wen ; Dept. of Radiol., State Univ. of New York, Stony Brook, NY, USA ; Tianfang Li ; Zhengrong Liang

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 gamma photons are attenuated inside the body before arriving at the detector. A quantitative reconstruction must consider the attenuation, which is usually nonuniform. Novikov has derived an explicit inversion formula for the nonuniformly attenuated Radon transform for SPECT reconstruction of parallel-beam collimated projections. In this paper, we extend his research to variable focal-length fan-beam VFF collimator geometry. A ray-driven analytical formula for VFF reconstruction with nonuniform attenuation was derived. As a unified framework, this formula can be used for parallel-beam, fan-beam, and VFF collimators. Its accuracy is demonstrated by computer simulation experiments.

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Nuclear Science, IEEE Transactions on  (Volume:50 ,  Issue: 5 )