Image reconstruction in SPECT with a half detector

In parallel beam computed tomography, the measured projections at conjugate views are mathematically identical, and, consequently, this symmetry can be exploited for reducing either the scanning angle or the size of the detector arrays. However, in single-photon emission computed tomography (SPECT), because the gamma-rays in the conjugate views suffer different photon attenuation, the measured projections at conjugate views are generally different. Therefore, it had been widely considered that projections measured data over a full angular range of 360 degrees and over the whole detector face are generally required for exactly reconstructing the distributions of gamma-ray emitters. Recently, it has been revealed that exact image can be reconstructed from projections acquired with a full detector over disjoint angular intervals whose summation is 180 degree when the attenuation medium is uniform. In this work, we show that exact SPECT images can also be reconstructed from projections over 360 degrees, but acquired with a half detector viewing half of the image space. We present an heuristic perspective that supports this claim for SPECT with both uniform and non-uniform attenuation.