Computational burden is a major concern when an iterative algorithm is used to reconstruct a three-dimensional (3-D) image with attenuation, detector response, and scatter corrections. Most of the computation time is spent executing the projector and backprojector of an iterative algorithm. Usually, the projector and the backprojector are transposed operators of each other. The projector should model the imaging geometry and physics as accurately as possible. Some researchers have used backprojectors that are computationally less expensive than the projectors to reduce computation time. This paper points out that valid backprojectors should satisfy a condition that the projector/backprojector matrix must not contain negative eigenvalues. This paper also investigates the effects when unmatched projector/backprojector pairs are used.

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The point response resolution of a gamma camera deteriorates with increased distance from the face of the collimator. This results in reconstruction artifacts that are seen as shape distortion and density non-uniformity. For parallel, fan, and cone beam geometries, iterative reconstruction algorithms have been developed which eliminate these artifacts by incorporating the three-dimensional spatially varying geometric point response into models for the projection and backprojection operations which also model photon attenuation. The algorithms have been tested on an IBM 3090-600s supercomputer. The iterative EM reconstruction algorithm is 50 times longer with geometric response and photon attenuation models than without modeling these physical effects. We have demonstrated an improvement in image quality in the reconstruction of projection data collected from a single photon emission computed tomography (SPECT) imaging system. Using phantom experiments, we observe that the modeling of the spatial system response imposes a smoothing without loss of resolution.

Echo-planar imaging (EPI) is very sensitive to patient-induced field inhomogeneity caused by susceptibility changes between different anatomical regions. This results in geometric and intensity distortions in the image, especially near tissue/air and tissue/bone interfaces. A new approach is presented to reduce geometric and intensity distortions in EPI. A phase-encoded multireference scan is used to estimate the amplitude and phase errors in the measured signals due to the field inhomogeneity. The EPI data is corrected using both the amplitude and phase of the measured errors. This technique has been evaluated using EPI pulse sequences implemented with conventional gradients and implemented with imaging systems that have special resonating gradients and fast analog to digital converters. The results in both phantom and human studies show that in the absence of object motion the new correction technique can effectively reduce the geometric and intensity distortions.

The Compton camera can collect SPECT data with high efficiency due to electronic collimation. The data acquired from a Compton camera are projections of source activity along cones and are approximated in this paper by cone-surface integrals. This paper proposes the use of an orthogonal spherical expansion to convert the cone-surface integrals into plane integrals. The conversion technique is efficient. Once the plane integrals are obtained, a 3D image can be reconstructed by the 3D Radon inversion formula. The algorithm is implemented and computer simulations are used to demonstrate the efficiency and accuracy of the proposed reconstruction algorithm.