Linear ridge regression with spatial constraint for generation of parametric images in dynamic positron emission tomography studies

Due to its simplicity, computational efficiency, and reliability, weighted linear regression (WLR) is widely used for generation of parametric imaging in positron emission tomography (PET) studies, but parametric images estimated by WLR usually have high image noise level. To improve the stability and signal-to-noise ratio of the estimated parametric images, we have added ridge regression, a statistical technique that reduces estimation variability at the expense of a small bias. To minimize the bias, spatially smoothed images obtained with WLR are used as a constraint for ridge regression. This new algorithm consists of two steps. First, parametric images are generated by WLR and are spatially smoothed. Ridge regression is then applied using the smoothed parametric images obtained in the first step as the constraint. Since both "generalized" ridge regression and "simple" ridge regression are used in statistical applications, we evaluated specifically in this study the relative advantages of the two when incorporated for generating parametric images from dynamic O-15 water PET studies. Computer simulations of a dynamic PET study with the spatial configuration of Hoffman's brain phantom and a real human PET study were used as the data for the evaluation. Results reveal ridge regressions improve image quality of parametric images for studies with high or middle noise level, as compared to WLR. Use of generalized ridge regression offers little advantage over that of simple ridge regression.