Analysis of Region of Interest Quantification for PET Image Reconstruction with Selective Regularization

Quantifying PET tracer uptake in a region of interest (ROI) is an important task in a variety of applications including brain imaging, myocardial imaging, and tumor activity assessment. Many post-reconstruction correction methods that compensate for spatial resolution or partial volume effects have been proposed for ROI quantification. Here our goal is to optimize the image reconstruction methods themselves for this task through the use of spatially variant regularization. We investigate and analyze a selective regularization strategy where reduced smoothing is imposed across the boundary of a pre-specified ROI which can be drawn, for example, from a coregistered CT image. Preliminary simulation results show that this strategy leads to better bias/variance trade-offs than spatially uniform regularization. However, the penalty function for selective smoothing is space-variant and therefore it is not straightforward to predict the bias and variance of ROI uptake estimators in a computationally efficient way without expensive Monte Carlo simulation. Here we develop a computationally efficient method to predict bias and variance through use of the Sherman-Morrison-Woodbury matrix identity and local Fourier approximations. Simulation results show that the prediction is reasonably accurate.