Fan-Beam Short Scan SPECT with Uniform Attenuation

It is well known that in fan-beam X-ray computed tomography (CT) projection data acquired over 2pi contain redundant information and that accurate and stable reconstruction can be obtained from less than 2pi data. In single photon emission computed tomography (SPECT), since the photon absorption is distance-dependent, the conjugate projections are not identical even in the absence of noise. However, projection data over 2pi are still redundant for a noiseless image reconstruction except that the redundancy is not as apparent as in X-ray CT. We study the redundant information in the fan-beam SPECT projection data in this work and developed a reconstruction algorithm only requiring data measured over a short scan. Experiment with computer-simulated data is performed to establish the validity and efficiency of the solution. Besides the explicit inversion formula, the most significant property of the algorithm is that truncations are allowed in the projection data along the detector at each view angle, which makes the reconstruction of region of interest (ROI) feasible in some particular geometries.