This paper describes a new filter for parametric images obtained from dynamic positron emission tomography (PET) studies. The filter is based on the wavelet transform following the heuristics of a previously published method that are here developed into a rigorous theoretical framework. It is shown that the space-time problem of modeling a dynamic PET sequence reduces to the classical one of estimation of a normal multivariate vector of independent wavelet coefficients that, under least-squares risk, can be solved by straightforward application of well established theory. From the study of the distribution of wavelet coefficients of PET images, it is inferred that a James-Stein linear estimator is more suitable for the problem than traditional nonlinear procedures that are incorporated in standard wavelet filters. This is confirmed by the superior performance of the James-Stein filter in simulation studies compared to a state-of-the-art nonlinear wavelet filter and a nonstationary filter selected from literature. Finally, the formal framework is interpreted for the practitioner's point of view and advantages and limitations of the method are discussed.

In this paper a clustering technique is proposed for attenuation correction (AC) in positron emission tomography (PET). The method is unsupervised and adaptive with respect to counting statistics in the transmission (TR) images. The technique allows the classification of pre- or post-injection TR images into main tissue components in terms of attenuation coefficients. The classified TR images are then forward projected to generate new TR sinograms to be used for AC in the reconstruction of the corresponding emission (EM) data. The technique has been tested on phantoms and clinical data of brain, heart and whole-body PET studies. The method allows: (a) reduction of noise propagation from TR into EM images, (b) reduction of TR scanning to a few minutes (3 min) with maintenance of the quantitative accuracy (within 6%) of longer acquisition scans (15-20 min), (c) reduction of the radiation dose to the patient, (d) performance of quantitative whole-body studies.

Quantitative measurement of tumor blood flow with [15O]water can be used to evaluate the effects of tumor treatment over time. Since quantitative flow measurements require an input function, we developed the profile fitting method (PFM) to measure the input function from positron emission tomography images of the aorta. First, a [11C]CO scan was acquired and the aorta region was analyzed. The aorta diameter was determined by fitting the image data with a model that includes scanner resolution, the measured venous blood radioactivity concentration, and the spillover of counts from the background. The diameter was used in subsequent fitting of [15O]water dynamic images to estimate the aorta and background radioactivity concentrations. Phantom experiments were performed to test the model. Image quantification biases (up to 15%) were found for small objects, particularly for those in a large elliptical phantom. However, the bias in the PFM concentration estimates was much smaller (2%-6%). A simulation study showed that PFM had less bias and/or variability in flow parameter estimates than an ROI method. PFM was applied to human [11C]CO and [15O]water dynamic studies with left ventricle input functions used as the gold standard. PFM parameter estimates had higher variability than found in the simulation but with minimal bias. These studies suggest that PFM is a promising technique for the noninvasive measurement of the aorta [15O]water input function.