The purpose of this study is to develop, implement and evaluate a 3D filtered back-projection (FBP) algorithm for SPECT using a multi-segment rotating slant-hole (RSH) collimator. Previously, we derived a 3D frequency-domain filter function used in a back-projection filtering (BPF) algorithm for multi-segment RSH SPECT. The 3D orientation of the projection direction from each segment, each collimator rotation angle and each collimator-camera position defines a 2D central section through the center of the 3D BPF reconstruction filter. For FBP, these central sections are determined analytically from the mathematical expression of 3D BPF filter, and are re-scaled and rotated before filtering the corresponding projections to avoid interpolation. The FBP algorithm was implemented to reconstruct simulated and experimentally acquired SPECT data from a four-segment RSH collimator. The reconstructed images were compared to those from BPF. The results of FBP are comparable to BPF, and with reduced low-intensity image artifacts. We conclude that FBP is a superior alternative to BPF for RSH SPECT. It provides accurate reconstruction in relatively short computing time. In addition, it requires less computer memory, permits on-the-fly image reconstruction during data acquisition, and may facilitate additional processing during reconstruction to reduce truncation artifacts.
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