Spatially varying regularization for motion compensated PET reconstruction

Motion-compensated PET reconstruction enables reduction of blurring artifacts in PET images caused by respiratory or cardiac motion without sacrificing signal-to-noise ratio. The motion-compensated image reconstruction problem can be solved using a maximum a posteriori (MAP) reconstruction scheme. It is well known that for the uniform quadratic penalty, MAP generates images with a spatially varying resolution. We present here a regularization approach to mitigate this effect by spatially adjusting the degree of smoothing in an automated fashion in the motion-compensated MAP reconstruction framework. Our method is based on an analytical approximation for the diagonal elements of the Fisher information matrix which can be used to control the local impulse response at each voxeI. We have applied the developed regularization scheme to respiratory gated studies on the NeAT torso phantom with simulated lung lesions. We compared our regularization scheme for multigate reconstruction with the uniform quadratic penalty, ungated reconstruction, and single-gate reconstruction. We show that for multi-gate reconstruction, both activity and motion influence the variance for each voxel of the reconstructed image. Accordingly our regularizer yields higher gains in contrast recovery relative to the UQP in lesions that move substantially during breathing.