Noise propagation in resolution modeled PET imaging and its impact on detectability

Positron emission tomography imaging is affected by a number of resolution degrading phenomena, including positron range, photon non-collinearity and inter-crystal blurring. An approach to this issue is to model some or all of these effects within the image reconstruction task, referred to as resolution modeling (RM). This approach is commonly observed to yield images of higher resolution and subsequently contrast, and can be thought of as improving the modulation transfer function. Nonetheless, RM can substantially alter the noise distribution. In this work, we utilize noise propagation models in order to accurately characterize the noise texture of reconstructed images in the presence of RM. Furthermore we consider the task of lesion or defect detection, which is highly determined by the noise distribution as quantified using the noise power spectrum. Ultimately, we use this framework to demonstrate why conventional trade-off analyses (e.g. contrast versus noise, using simplistic noise metrics) do not provide a complete picture of the impact of RM and that improved performance of RM according to such analyses does not necessarily translate to the superiority of RM in detection task performance.