π-scheme short-scan SPECT and image reconstruction with nonuniform attenuation

Because the effects of physical factors such as photon attenuation and spatial resolution are distance-dependent in single-photon emission computed tomography (SPECT), it is generally considered that accurate image reconstruction requires knowledge of the data function over 2π. In SPECT with only uniform attenuation, Noo and Wagner (2001) recently showed that an accurate image can be reconstructed from knowledge of the data function over the interval [0, π]. In this work, we consider image reconstruction in π-scheme SPECT with nonuniform attenuation. In its most general form, π-scheme SPECT entails data acquisition over disjoint angular intervals without conjugate views, totaling to π radians. We develop an heuristic perspective for observing that the data function in full-scan SPECT contains redundant information and that the data function in π-scheme SPECT contains complete information necessary for accurate image reconstruction. We conduct simulation studies in which the expectation maximization algorithm is used for image reconstruction from the data acquired in π-scheme SPECT with nonuniform attenuation. The results in these simulation studies seem to corroborate hypothesis that accurate images can be reconstructed from π-scheme data. π-scheme SPECT allows data acquisition over different combinations of disjoint angular intervals, thereby providing a flexibility in choosing projection views at which the emitted gamma-rays may undergo the least attenuation and blurring. It should be stressed, however, that the proposed perspective on redundant information is intended only to heuristically reveal the data redundancy in SPECT with nonuniform attenuation and that it has not been demonstrated mathematically to guarantee the stability and exactness of image reconstruction from the π-scheme data.