In this study, we investigate the application of multi-parametric anato-functional (MR-PET) priors for the maximum a posteriori (MAP) reconstruction of brain PET data in order to address the limitations of the conventional anatomical priors in the presence of PET-MR mismatches. In addition to partial volume correction benefits, the suitability of these priors for reconstruction of low-count PET data is also introduced and demonstrated, comparing to standard maximum-likelihood (ML) reconstruction of high-count data. The conventional local Tikhonov and total variation (TV) priors and current state-of-the-art anatomical priors including the Kaipio, non-local Tikhonov prior with Bowsher and Gaussian similarity kernels are investigated and presented in a unified framework. The Gaussian kernels are calculated using both voxel- and patch-based feature vectors. To cope with PET and MR mismatches, the Bowsher and Gaussian priors are extended to multi-parametric priors. In addition, we propose a modified joint Burg entropy prior that by definition exploits all parametric information in the MAP reconstruction of PET data. The performance of the priors was extensively evaluated using 3D simulations and two clinical brain datasets of [F]florbetaben and [F]FDG radiotracers. For simulations, several anato-functional mismatches were intentionally introduced between the PET and MR images, and furthermore, for the FDG clinical dataset, two PET-unique active tumours were embedded in the PET data. Our simulation results showed that the joint Burg entropy prior far outperformed the conventional anatomical priors in terms of preserving PET unique lesions, while still reconstructing functional boundaries with corresponding MR boundaries. In addition, the multi-parametric extension of the Gaussian and Bowsher priors led to enhanced preservation of edge and PET unique features and also an improved bias-variance performance. In agreement with the simulation results, the clinical results also showed that the Gaussian prior with voxel-based feature vectors, the Bowsher and the joint Burg entropy priors were the best performing priors. However, for the FDG dataset with simulated tumours, the TV and proposed priors were capable of preserving the PET-unique tumours. Finally, an important outcome was the demonstration that the MAP reconstruction of a low-count FDG PET dataset using the proposed joint entropy prior can lead to comparable image quality to a conventional ML reconstruction with up to 5 times more counts. In conclusion, multi-parametric anato-functional priors provide a solution to address the pitfalls of the conventional priors and are therefore likely to increase the diagnostic confidence in MR-guided PET image reconstructions.

Abstract-PET image reconstruction is highly susceptible to the impact of Poisson noise, and if shorter acquisition times or reduced injected doses are used, the noisy PET data become even more limiting. The recent development of kernel expectation maximisation (KEM) is a simple way to reduce noise in PET images, and we show in this work that impressive dose reduction can be achieved when the kernel method is used with MR-derived kernels. The kernel method is shown to surpass maximum likelihood expectation maximisation (MLEM) for the reconstruction of low-count datasets (corresponding to those obtained at reduced injected doses) producing visibly clearer reconstructions for unsmoothed and smoothed images, at all count levels. The kernel EM reconstruction of 10% of the data had comparable whole brain voxel-level error measures to the MLEM reconstruction of 100% of the data (for simulated data, at 100 iterations). For regional metrics, the kernel method at reduced dose levels attained a reduced coefficient of variation and more accurate mean values compared to MLEM. However, the advances provided by the kernel method are at the expense of possible over-smoothing of features unique to the PET data. Further assessment on clinical data is required to determine the level of dose reduction that can be routinely achieved using the kernel method, whilst maintaining the diagnostic utility of the scan.

In this paper, we propose a generalized joint sparsity regularization prior and reconstruction framework for the synergistic reconstruction of positron emission tomography (PET) and under sampled sensitivity encoded magnetic resonance imaging data with the aim of improving image quality beyond that obtained through conventional independent reconstructions. The proposed prior improves upon the joint total variation (TV) using a non-convex potential function that assigns a relatively lower penalty for the PET and MR gradients, whose magnitudes are jointly large, thus permitting the preservation and formation of common boundaries irrespective of their relative orientation. The alternating direction method of multipliers (ADMM) optimization framework was exploited for the joint PET-MR image reconstruction. In this framework, the joint maximum a posteriori objective function was effectively optimized by alternating between well-established regularized PET and MR image reconstructions. Moreover, the dependency of the joint prior on the PET and MR signal intensities was addressed by a novel alternating scaling of the distribution of the gradient vectors. The proposed prior was compared with the separate TV and joint TV regularization methods using extensive simulation and real clinical data. In addition, the proposed joint prior was compared with the recently proposed linear parallel level sets (PLSs) method using a benchmark simulation data set. Our simulation and clinical data results demonstrated the improved quality of the synergistically reconstructed PET-MR images compared with the unregularized and conventional separately regularized methods. It was also found that the proposed prior can outperform both the joint TV and linear PLS regularization methods in assisting edge preservation and recovery of details, which are otherwise impaired by noise and aliasing artifacts. In conclusion, the proposed joint sparsity regularization within the presented a ADMM reconstruction framework is a promising technique, nonetheless our clinical results showed that the clinical applicability of joint reconstruction might be limited in current PET-MR scanners, mainly due to the lower resolution of PET images.