Maximum likelihood reconstruction for converging beam SPECT with a displaced center-of-rotation

The authors describe the implementation of a maximum likelihood (ML) algorithm using expectation maximization (EM) for cone beam (CB) and pinhole (PH) SPECT with a displaced center-of-rotation (COR). A ray-tracing technique is used in implementing the MLEM algorithm. The difference between CB and PH collimation is discussed. The COR displacement is the displacement of the midplane of the collimators off the rotation center and is characterized by two orthogonal components: the shift of the midplane of the collimators along the direction of the axis-of-rotation (AOR), η, and the distance between the midline of the collimators and the AOR, τ. The proposed ML-EM algorithm corrects the COR displacement by incorporating it into the ray-tracing process. The algorithm is tested using experimentally acquired data and the results demonstrate that with the correction the ML-EM algorithm is able to correct artifacts associated with the COR displacement. By using detection systems with different resolutions (FWHM ~2 mm vs. 10 mm), the authors also demonstrate the greater importance of correcting even a small COR displacement with the increasing system resolution