Short-scan SPECT imaging with non-uniform attenuation and 3D distance-dependent spatial resolution

Abstract

Image quality and quantitative accuracy in single-photon emission computed tomography (SPECT) can be degraded by, e.g., the effects of photon attenuation and finite spatial resolution. It is generally considered that adequate compensation for such effects on SPECT images requires data acquired over 2π. Recently, using the existing consistency condition on the data function, Noo and Wagner (2001 Inverse Problems 17 1357–72) have shown analytically that data acquired over only π can be used to correct completely for the effect of uniform attenuation in SPECT. It remains unknown, however, whether data acquired only over π in SPECT with non-uniform attenuation and/or 3D distance-dependent spatial resolution (DDSR) contain complete information for accurate image reconstruction. In this work, we develop a heuristic perspective, which is referred to as the potato peeler perspective, to show conceptually that data in SPECT with non-uniform attenuation and/or 3D DDSR acquired over 2π contain redundant information and that such information can be used to reduce the scanning angle in SPECT. Specifically, we show heuristically that, in SPECT with only non-uniform attenuation, the scanning angle can be reduced from 2π to π and that, in SPECT with both non-uniform attenuation and DDSR with a physically realistic form, the scanning angle can be reduced from 2π to π in a practical sense. We conduct computer simulation studies, and the results from these studies corroborate the observations obtained based upon the heuristic potato peeler perspective.