Image Reconstruction in 3D Short-Scan SPECT

Physical factors such as photon attenuation degrade image quality and quantitative accuracy in single-photon emission computed tomography (SPECT). It is often considered (especially in situations with non-uniform attenuation and distance-dependent spatial resolution (DDSR)) that adequate compensation for the effects of these physical factors requires data acquired over 2 . However, as the analysis in this work suggests, one may need data acquired only over to correct adequately for the effects of some of the physical factors. Reduction of the scanning angle in SPECT imaging is desirable because it can reduce the scanning time and thus minimize patient-motion and other artifacts, and because scans over less than 2 can allow the detector to be rotated at a fixed distance closer to the patient. Also, in certain cases (e.g., in cardiac SPECT), one can choose the scanning angular range for obtaining maximum numbers of photons. This work focuses on investigation of accurate image reconstruction in 3D SPECT from data that are acquired with parallel-beam collimation only over and that contain the effects of photon attenuation (either uniform or non-uniform) and DDSR. For simplicity, we refer to such a scanning configuration as 3D short-scan SPECT. This work may have significant theoretical as well as practical implications for image reconstruction in SPECT. I. BACKGROUND Single-photon emission computed tomography (SPECT) is an important nuclear medicine imaging modality. Physical factors in SPECT such as photon attenuation and imperfect spatial resolution degrade image quality and quantitative accuracy [1,2] and should be adequately corrected for. Because these physical factors are generally spatially variant, it is often considered (especially in the situation with non-uniform attenuation and distance-dependent spatial resolution (DDSR)) that adequate compensation for the effects of these physical factors requires data measured at projection angles over 2 . However, as the analysis below suggests, it appears possible that (at least under certain conditions) data acquired only over can be used for adequately correcting for the effects of some physical factors such as photon attenuation. The reduction of the scanning angle in SPECT imaging is desirable because it can reduce scanning time and thereby minimize patientmotion and other artifacts. Also, in certain cases (e.g., in cardiac SPECT), one can choose the scanning angular range for obtaining maximum numbers of photons [3, 4]. This work focuses on investigation of accurate image reconstruction in 3D SPECT from data that are acquired with parallel-beam collimation only over and that contain the effects of photon attenuation (either uniform or non-uniform) and DDSR. For simplicity, we refer to such a scanning configuration as the 3D short-scan SPECT. II. MATHEMATICAL RATIONALES A. Redundant Information and Reduction of Scanning Angle In some tomographic imaging systems, the data measured over contain redundant information. One example is measurement of the 2D Radon transform [5], , of a real function over , where is the detector bin index and is the measurement angle. Such measurements contain redundant information because, in the absence of noise and other inconsistencies, the measurements from conjugate views are mathematically identical, i.e., (1) It is well known that such information can be exploited for reducing the scanning angle from to because the maximum difference between the values of the real angles on the two sides of Eq. (1) is . In fan-beam computed tomography (CT), the quantity is used to denote the measured transmission data, where indicates the detector bin index and the measurement angle. Although the fan-beam measurements (except for those with ) from conjugate views are not mathematically identical, one can still show that the fan-beam data acquired over contains redundant information, i.e., ! " $# (2) where # is a known and real function of , and its explicit form depends upon the detector configurations [6, 7]. It can be shown that %'&)( * $#