Detection and correction of rigid patient motion in SPECT with exponential data consistency conditions

Objective Rigid patient motion during single photon emission computed tomography (SPECT) can introduce artifacts in the reconstructed images. Patient translation can be estimated using various data-driven methods, e.g., those based on exponential data consistency conditions (eDCCs). eDCCs are mathematical equations that characterize the small redundancy between pairs of exponential projections derived from the application of the attenuated Radon transform. However, rigid motion typically involves both translational and rotational components. This study aimed to develop and evaluate an eDCCs-based approach for detecting and estimating any rigid patient motion during a SPECT acquisition. Approach We calculated exponential projections from SPECT measurements, assuming that the photon emission was confined to a known convex region K with constant attenuation, and evaluated their pairwise consistency with eDCCs. The rigid motion was characterized by six parameters, three translations and three rotations, and the index indicating when the motion occurred. The six parameters and the motion index were estimated by minimizing the inconsistency between pairs of exponential projections after compensating for the estimated rigid motion in the projection domain. The method was evaluated on several datasets of a simulated liver patient and on experimentally acquired data of a NEMA IEC phantom. Main results The proposed method accurately estimated the ground truth motion parameters when the SPECT projections were ideally modeled by the attenuated Radon transform, but was affected by degrading physical effects, mainly by the system spatial resolution (intrinsic and collimator spatial resolution) and the scatter. Despite these physical effects, eDCCs recovered the source center position within a two-pixel offset and substantially improved reconstructed image quality. Specifically, the method achieved a relative activity recovery coefficient (rARC) of around 101% relative to images reconstructed from motion-free projections, compared with an rARC of 87% without correction for the studied liver patient's rigid motion occurring at the beginning of the acquisition. Significant A fully data-driven method with eDCCs was able to estimate and correct for a rigid patient motion during a SPECT acquisition.