Evaluation of Parallel Level Sets and Bowsher’s Method as Segmentation-Free Anatomical Priors for Time-of-Flight PET Reconstruction

Abstract

In this article, we evaluate Parallel Level Sets (PLS) and Bowsher's method as segmentation-free anatomical priors for regularized brain positron emission tomography (PET) reconstruction. We derive the proximity operators for two PLS priors and use the EM-TV algorithm in combination with the first order primal-dual algorithm by Chambolle and Pock to solve the non-smooth optimization problem for PET reconstruction with PLS regularization. In addition, we compare the performance of two PLS versions against the symmetric and asymmetric Bowsher priors with quadratic and relative difference penalty function. For this aim, we first evaluate reconstructions of 30 noise realizations of simulated PET data derived from a real hybrid positron emission tomography/magnetic resonance imaging (PET/MR) acquisition in terms of regional bias and noise. Second, we evaluate reconstructions of a real brain PET/MR data set acquired on a GE Signa time-of-flight PET/MR in a similar way. The reconstructions of simulated and real 3D PET/MR data show that all priors were superior to post-smoothed maximum likelihood expectation maximization with ordered subsets (OSEM) in terms of bias-noise characteristics in different regions of interest where the PET uptake follows anatomical boundaries. Our implementation of the asymmetric Bowsher prior showed slightly superior performance compared with the two versions of PLS and the symmetric Bowsher prior. At very high regularization weights, all investigated anatomical priors suffer from the transfer of non-shared gradients.

Intercomparison of MR-Informed Methods for PET Image Reconstruction

“…The gray and white matter tissue classes were assigned intensities with the ratio of 4:1 in keeping with the expected uptake from an FDG tracer. 30,60,61 Real PET images have more structural variation than the produced piecewise constant simulated phantom. To discourage overly piecewise constant images, Gaussian smoothed random structures were incorporated into the simulated PET phantom, in accordance with Eq.…”

“…For such reasons, the consequence of varying penalty functions (for instance using the relative difference instead of the quadratic penalty function) while including image-weighting factors in the prior has been shown to be minimal. 30 The selection of MR(only)-informed weighting factors under comparison in this work is the Gaussian similarity kernel 31,32 and the asymmetric Bowsher prior, 5 due to their enduring popularity, and ability to match the performance of more involved MR-informed methods. 30,33,34 In addition, these methods use spatial similarity matrices to extract MR structures, in a comparable way to the kernel methods.…”

“…30 The selection of MR(only)-informed weighting factors under comparison in this work is the Gaussian similarity kernel 31,32 and the asymmetric Bowsher prior, 5 due to their enduring popularity, and ability to match the performance of more involved MR-informed methods. 30,33,34 In addition, these methods use spatial similarity matrices to extract MR structures, in a comparable way to the kernel methods. Thus, all methods investigated in this study can be considered to be part of the same group of algorithms which include MR information through similarity matrices.…”

“…6,[40][41][42][43][44] Despite these beneficial properties achieved through the inclusion of MR information, adverse consequences also arise, such as increased susceptibility to suppressing PET-unique high-intensity regions. 10,30 This is a major pitfall for the visual diagnostic interpretation of PET images, in particular for oncological cases, where PET imaging has been shown to improve the diagnosis and subsequent treatment of cancers. 45 Specifically, for brain and neck cancers [ 18 F]FDG PET has played an increasing role in the diagnosis and planning.…”

Faster PET reconstruction with non-smooth priors by randomization and preconditioning

“…Non-smooth priors can also be used to either incorporate anatomical knowledge from MRI or CT into the reconstruction, e.g. [12,[24][25][26][27][28], or to jointly reconstruct PET and the anatomical CT/MRI image [29][30][31][32]. Only a few optimization algorithms are capable of combining non-smooth priors and the Poisson noise model, e.g.…”