Detection and correction of translational motion in SPECT with exponential data consistency conditions.

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Rigid patient motion can cause artifacts in single photon emission computed tomography (SPECT) images, compromising the diagnosis and treatment planning. Exponential data consistency conditions (eDCCs) are mathematical equations describing the redundancy of exponential SPECT measurements. It has been recently shown that eDCCs can be used to detect patient motion in SPECT projections.
 This study aimed at developing a fully data-driven method based on eDCCs to estimate and correct for translational motion in SPECT.
 If all activity is encompassed inside a convex region K of constant attenuation, eDCCs can be derived from SPECT projections and can be used to verify the pair-wise consistency of these projections. Our method assumes a single patient translation between two detector gantry positions. The proposed method estimates both the three-dimensional shift and the motion index, i.e. the index of the first gantry position after motion occurred. The estimation minimizes the eDCCs between the subset of projections before the motion index and the subset of motion-corrected projections after the motion index. We evaluated the proposed method using Monte Carlo simulated and experimental data of a NEMA IEC phantom and simulated projections of a liver patient. The method's robustness was assessed by applying various motion vectors and motion indices.
 Motion detection and correction with eDCCs were sensitive to movements above 3~mm.
The accuracy of the estimation was below the 2.39~mm pixel spacing with good precision in all studied cases. The proposed method led to a significant improvement in the quality of reconstructed SPECT images. The activity recovery coefficient relative to the SPECT image without motion was above 90\% on average over the six spheres of the NEMA IEC phantom and 97\% for the liver patient. For example, for a (2,2,2)~cm translation in the middle of the liver acquisition, the activity recovery coefficient was improved from 35\% (non-corrected projections) to 99\% (motion-corrected projections).
The study proposed and demonstrated the good performance of translational motion detection and correction with eDCCs in SPECT acquisition data.