Image reconstruction with a half-detector in single-photon emission computed tomography with nonuniform attenuation

In parallel beam computed tomography, measured projections at conjugate views are mathematically identical. This symmetry can be exploited for either reducing the scanning angle or the size of the detector arrays. In single-photon emission computed tomography (SPECT), because the gamma rays in the conjugate views suffer different photon attenuation, measured projections at conjugate views are generally different. Therefore, it had been widely considered that projections covering 360 deg and the whole detector face are required for exact reconstruction of the distributions of gamma-ray emitters. In this work, we show that projections covering 360 deg, but acquired with a half-detector viewing half of the image space, provide the necessary information to reconstruct a unique image in SPECT with nonuniform attenuation.