Non-Gaussian smoothing of low-count transmission scans for PET whole-body studies

A non-Gaussian smoothing (NGS) technique is developed for filtering low count transmission (TR) data to be used for attenuation correction (AC) of positron emission tomography (PET) studies. The method is based on a statistical technique known as the generalized linear mixed model that allows an inverse link function that avoids the inversion of the observed transmission data. The NGS technique has been implemented in the sinogram domain in one-dimensional mode as angle-by-angle computation. To make it adaptive as a function of the TR count statistics we also develop and validate an objective procedure to choose an optimal smoothing parameter. The technique is assessed using experimental phantoms, simulating PET whole-body studies, and applied to real patient data. Different experimental conditions, in terms of TR scan time (from 1 h to 1 min), covering a wide range of TR counting statistic are considered. The method is evaluated, in terms of mean squared error (MSE), by comparing pixel by pixel the distribution for high counts statistics TR scan (1 h) with the corresponding counts distribution for low count statistics TR scans (e.g., 1 min). The smoothing parameter selection is shown to have high efficiency, meaning that it tends to choose values close to the unknown best value. Furthermore, the counts distribution of emission (EM) images, reconstructed with AC generated using low count TR data (1 min), are within 5% of the corresponding EM images reconstructed with AC generated using the high count statistics TR data (1 h). An application to a real patient whole-body PET study shows the promise of the technique for routine use.