Correcting fast irregular motion in PET: maximum-likelihood motion and activity (MLMA) reconstruction

Purpose: Positron emission tomography (PET) imaging naturally suffers from motion blur due to long acquisitions. As such, motion-compensation provides a promising solution to improve image quality. Traditional methods for motion-correction often involve a combination of gating and data-binning, assuming that motion is periodic, to accumulate sufficient counts per motion-state frame. Irregular motion can be estimated but it requires complex motion-capture systems or elaborate data-driven algorithms, which are difficult to configure (physical or model setup) and hampered by the high noise of short timeframes. We propose a new method that alternatingly estimates and corrects for motion at high temporal frequency in PET imaging: Maximum-Likelihood Motion and Activity (MLMA) reconstruction. MLMA estimates both the time-series of deformation vector fields and the motion-corrected activity image for the whole acquisition. Together, this allows to visualize anatomical structures moving in time. Methods: The method exploits the high compressibility and spatial smoothness of motion through a cubic B-spline motion-model and through spatial regularization. MLMA was configured to 2 Hz resolution and applied on (A) the digital XCAT phantom, (B) acquisitions of a moving anthropomorphic torso phantom and (C) clinical patient data. Results: The results show that MLMA can accurately correct motion at high frequency (2 Hz), with subvoxel accuracy (up to 2.5 mm root-mean-square error (RMSE) on 4 mm isotropic voxels) and realistic breathing (amplitude range 14.7 mm and average period 4.5 s). This enables visually-noticeable improvements on image quality. Conclusion: The proposed MLMA reconstruction method resolves the motion encoded in very-short PET timeframes, irrespective of the very low counts and noise inherent to PET projection data.