Evaluation of three MRI-based anatomical priors for quantitative PET brain imaging

Technical and instrumentational foundations of PET/MRI

This paper highlights the origins of combined positron emission tomography (PET) and magnetic resonance imaging (MRI) whole-body systems that were first introduced for applications in humans in 2010. This text first covers basic aspects of each imaging modality before describing the technical and methodological challenges of combining PET and MRI within a single system. After several years of development, combined and even fully-integrated PET/MRI systems have become available and made their way into the clinic. This multi-modality imaging system lends itself to the advanced exploration of diseases to support personalized medicine in a long run. To that extent, this paper provides an introduction to PET/MRI methodology and important technical solutions.

Noise suppressed partial volume correction for cardiac SPECT/CT

PURPOSE

Partial volume correction (PVC) methods typically improve quantification at the expense of increased image noise and reduced reproducibility. In this study, the authors developed a novel voxel-based PVC method that incorporates anatomical knowledge to improve quantification while suppressing noise for cardiac SPECT/CT imaging.

METHODS

In the proposed method, the SPECT images were first reconstructed using anatomical-based maximum a posteriori (AMAP) with Bowsher's prior to penalize noise while preserving boundaries. A sequential voxel-by-voxel PVC approach (Yang's method) was then applied on the AMAP reconstruction using a template response. This template response was obtained by forward projecting a template derived from a contrast-enhanced CT image, and then reconstructed using AMAP to model the partial volume effects (PVEs) introduced by both the system resolution and the smoothing applied during reconstruction. To evaluate the proposed noise suppressed PVC (NS-PVC), the authors first simulated two types of cardiac SPECT studies: a (99m)Tc-tetrofosmin myocardial perfusion scan and a (99m)Tc-labeled red blood cell (RBC) scan on a dedicated cardiac multiple pinhole SPECT/CT at both high and low count levels. The authors then applied the proposed method on a canine equilibrium blood pool study following injection with (99m)Tc-RBCs at different count levels by rebinning the list-mode data into shorter acquisitions. The proposed method was compared to MLEM reconstruction without PVC, two conventional PVC methods, including Yang's method and multitarget correction (MTC) applied on the MLEM reconstruction, and AMAP reconstruction without PVC.

RESULTS

The results showed that the Yang's method improved quantification, however, yielded increased noise and reduced reproducibility in the regions with higher activity. MTC corrected for PVE on high count data with amplified noise, although yielded the worst performance among all the methods tested on low-count data. AMAP effectively suppressed noise and reduced the spill-in effect in the low activity regions. However it was unable to reduce the spill-out effect in high activity regions. NS-PVC yielded superior performance in terms of both quantitative assessment and visual image quality while improving reproducibility.

CONCLUSIONS

The results suggest that NS-PVC may be a promising PVC algorithm for application in low-dose protocols, and in gated and dynamic cardiac studies with low counts.

Analysis of partial volume correction on quantification and regional heterogeneity in cardiac PET

BACKGROUND

The partial volume correction (PVC) of cardiac PET datasets using anatomical side information during reconstruction is appealing but not straightforward. Other techniques, which do not make use of additional anatomical information, could be equally effective in improving the reconstructed myocardial activity.

METHODS

Resolution modeling in combination with different noise suppressing priors was evaluated as a means to perform PVC. Anatomical priors based on a high-resolution CT are compared to non-anatomical, edge-preserving priors (relative difference and total variation prior). The study is conducted on ex vivo datasets from ovine hearts. A simulation study additionally clarifies the relationship between prior effectiveness and myocardial wall thickness.

RESULTS

Simple resolution modeling during data reconstruction resulted in over- and underestimation of activity, which hampers the absolute left ventricular quantification when compared to the ground truth. Both the edge-preserving and the anatomy-based PVC techniques improve the absolute quantification, with comparable results (Student t-test, P = .17). The relative tracer distribution was preserved with any reconstruction technique (repeated ANOVA, P = .98).

CONCLUSIONS

The use of edge-preserving priors emerged as optimal choice for quantification of tracer uptake in the left ventricular wall of the available datasets. Anatomical priors visually outperformed edge-preserving priors when the thinnest structures were of interest.

Joint MR-PET Reconstruction Using a Multi-Channel Image Regularizer

While current state of the art MR-PET scanners enable simultaneous MR and PET measurements, the acquired data sets are still usually reconstructed separately. We propose a new multi-modality reconstruction framework using second order Total Generalized Variation (TGV) as a dedicated multi-channel regularization functional that jointly reconstructs images from both modalities. In this way, information about the underlying anatomy is shared during the image reconstruction process while unique differences are preserved. Results from numerical simulations and in-vivo experiments using a range of accelerated MR acquisitions and different MR image contrasts demonstrate improved PET image quality, resolution, and quantitative accuracy.

Anatomically-aided PET reconstruction using the kernel method

This paper extends the kernel method that was proposed previously for dynamic PET reconstruction, to incorporate anatomical side information into the PET reconstruction model. In contrast to existing methods that incorporate anatomical information using a penalized likelihood framework, the proposed method incorporates this information in the simpler maximum likelihood (ML) formulation and is amenable to ordered subsets. The new method also does not require any segmentation of the anatomical image to obtain edge information. We compare the kernel method with the Bowsher method for anatomically-aided PET image reconstruction through a simulated data set. Computer simulations demonstrate that the kernel method offers advantages over the Bowsher method in region of interest quantification. Additionally the kernel method is applied to a 3D patient data set. The kernel method results in reduced noise at a matched contrast level compared with the conventional ML expectation maximization algorithm.

PET Reconstruction With an Anatomical MRI Prior Using Parallel Level Sets

The combination of positron emission tomography (PET) and magnetic resonance imaging (MRI) offers unique possibilities. In this paper we aim to exploit the high spatial resolution of MRI to enhance the reconstruction of simultaneously acquired PET data. We propose a new prior to incorporate structural side information into a maximum a posteriori reconstruction. The new prior combines the strengths of previously proposed priors for the same problem: it is very efficient in guiding the reconstruction at edges available from the side information and it reduces locally to edge-preserving total variation in the degenerate case when no structural information is available. In addition, this prior is segmentation-free, convex and no a priori assumptions are made on the correlation of edge directions of the PET and MRI images. We present results for a simulated brain phantom and for real data acquired by the Siemens Biograph mMR for a hardware phantom and a clinical scan. The results from simulations show that the new prior has a better trade-off between enhancing common anatomical boundaries and preserving unique features than several other priors. Moreover, it has a better mean absolute bias-to-mean standard deviation trade-off and yields reconstructions with superior relative l²-error and structural similarity index. These findings are underpinned by the real data results from a hardware phantom and a clinical patient confirming that the new prior is capable of promoting well-defined anatomical boundaries.

Postreconstruction filtering of 3D PET images by using weighted higher-order singular value decomposition

Background

Positron emission tomography (PET) always suffers from high levels of noise due to the constraints of the injected dose and acquisition time, especially in the studies of dynamic PET imaging. To improve the quality of PET image, several approaches have been introduced to suppress noise. However, traditional filters often blur the image edges, or erase small detail, or rely on multiple parameters. In order to solve such problems, nonlocal denoising methods have been adapted to denoise PET images.

Methods

In this paper, we propose to use the weighted higher-order singular value decomposition for PET image denoising. We first modeled the noise in the PET image as Poisson distribution. Then, we transformed the noise to an additive Gaussian noise by use of the anscombe root transformation. Finally, we denoised the transformed image using the proposed higher-order singular value decomposition (HOSVD)-based algorithms. The denoised results were compared with results from some general filters by performing physical phantom and mice studies.

Results

Compared to other commonly used filters, HOSVD-based denoising algorithms can preserve boundaries and quantitative accuracy better. The spatial resolution and the low activity features in PET image also can be preserved by use of HOSVD-based methods. Comparing with the standard HOSVD-based algorithm, the proposed weighted HOSVD algorithm can suppress the stair-step artifact, and the time-consumption is about half of that needed by the Wiener-augmented HOSVD algorithm.

Conclusions

The proposed weighted HOSVD denoising algorithm can suppress noise while better preserving of boundary and quantity in PET images.

Electronic supplementary material

The online version of this article (doi:10.1186/s12938-016-0221-y) contains supplementary material, which is available to authorized users.

Multi-Level Canonical Correlation Analysis for Standard-Dose PET Image Estimation

Positron emission tomography (PET) images are widely used in many clinical applications, such as tumor detection and brain disorder diagnosis. To obtain PET images of diagnostic quality, a sufficient amount of radioactive tracer has to be injected into a living body, which will inevitably increase the risk of radiation exposure. On the other hand, if the tracer dose is considerably reduced, the quality of the resulting images would be significantly degraded. It is of great interest to estimate a standard-dose PET (S-PET) image from a low-dose one in order to reduce the risk of radiation exposure and preserve image quality. This may be achieved through mapping both S-PET and low-dose PET data into a common space and then performing patch-based sparse representation. However, a one-size-fits-all common space built from all training patches is unlikely to be optimal for each target S-PET patch, which limits the estimation accuracy. In this paper, we propose a data-driven multi-level canonical correlation analysis scheme to solve this problem. In particular, a subset of training data that is most useful in estimating a target S-PET patch is identified in each level, and then used in the next level to update common space and improve estimation. In addition, we also use multi-modal magnetic resonance images to help improve the estimation with complementary information. Validations on phantom and real human brain data sets show that our method effectively estimates S-PET images and well preserves critical clinical quantification measures, such as standard uptake value.

Prediction of standard-dose brain PET image by using MRI and low-dose brain [18F]FDG PET images

PURPOSE

Positron emission tomography (PET) is a nuclear medical imaging technology that produces 3D images reflecting tissue metabolic activity in human body. PET has been widely used in various clinical applications, such as in diagnosis of brain disorders. High-quality PET images play an essential role in diagnosing brain diseases/disorders. In practice, in order to obtain high-quality PET images, a standard-dose radionuclide (tracer) needs to be used and injected into a living body. As a result, it will inevitably increase the patient's exposure to radiation. One solution to solve this problem is predicting standard-dose PET images using low-dose PET images. As yet, no previous studies with this approach have been reported. Accordingly, in this paper, the authors propose a regression forest based framework for predicting a standard-dose brain [(18)F]FDG PET image by using a low-dose brain [(18)F]FDG PET image and its corresponding magnetic resonance imaging (MRI) image.

METHODS

The authors employ a regression forest for predicting the standard-dose brain [(18)F]FDG PET image by low-dose brain [(18)F]FDG PET and MRI images. Specifically, the proposed method consists of two main steps. First, based on the segmented brain tissues (i.e., cerebrospinal fluid, gray matter, and white matter) in the MRI image, the authors extract features for each patch in the brain image from both low-dose PET and MRI images to build tissue-specific models that can be used to initially predict standard-dose brain [(18)F]FDG PET images. Second, an iterative refinement strategy, via estimating the predicted image difference, is used to further improve the prediction accuracy.

RESULTS

The authors evaluated their algorithm on a brain dataset, consisting of 11 subjects with MRI, low-dose PET, and standard-dose PET images, using leave-one-out cross-validations. The proposed algorithm gives promising results with well-estimated standard-dose brain [(18)F]FDG PET image and substantially enhanced image quality of low-dose brain [(18)F]FDG PET image.

CONCLUSIONS

In this paper, the authors propose a framework to generate standard-dose brain [(18)F]FDG PET image using low-dose brain [(18)F]FDG PET and MRI images. Both the visual and quantitative results indicate that the standard-dose brain [(18)F]FDG PET can be well-predicted using MRI and low-dose brain [(18)F]FDG PET.

MR-guided dynamic PET reconstruction with the kernel method and spectral temporal basis functions

Recent advances in dynamic positron emission tomography (PET) reconstruction have demonstrated that it is possible to achieve markedly improved end-point kinetic parameter maps by incorporating a temporal model of the radiotracer directly into the reconstruction algorithm. In this work we have developed a highly constrained, fully dynamic PET reconstruction algorithm incorporating both spectral analysis temporal basis functions and spatial basis functions derived from the kernel method applied to a co-registered T1-weighted magnetic resonance (MR) image. The dynamic PET image is modelled as a linear combination of spatial and temporal basis functions, and a maximum likelihood estimate for the coefficients can be found using the expectation-maximization (EM) algorithm. Following reconstruction, kinetic fitting using any temporal model of interest can be applied. Based on a BrainWeb T1-weighted MR phantom, we performed a realistic dynamic [(18)F]FDG simulation study with two noise levels, and investigated the quantitative performance of the proposed reconstruction algorithm, comparing it with reconstructions incorporating either spectral analysis temporal basis functions alone or kernel spatial basis functions alone, as well as with conventional frame-independent reconstruction. Compared to the other reconstruction algorithms, the proposed algorithm achieved superior performance, offering a decrease in spatially averaged pixel-level root-mean-square-error on post-reconstruction kinetic parametric maps in the grey/white matter, as well as in the tumours when they were present on the co-registered MR image. When the tumours were not visible in the MR image, reconstruction with the proposed algorithm performed similarly to reconstruction with spectral temporal basis functions and was superior to both conventional frame-independent reconstruction and frame-independent reconstruction with kernel spatial basis functions. Furthermore, we demonstrate that a joint spectral/kernel model can also be used for effective post-reconstruction denoising, through the use of an EM-like image-space algorithm. Finally, we applied the proposed algorithm to reconstruction of real high-resolution dynamic [(11)C]SCH23390 data, showing promising results.

The Use of Anatomical Information for Molecular Image Reconstruction Algorithms: Attenuation/Scatter Correction, Motion Compensation, and Noise Reduction

PET and SPECT are important tools for providing valuable molecular information about patients to clinicians. Advances in nuclear medicine hardware technologies and statistical image reconstruction algorithms enabled significantly improved image quality. Sequentially or simultaneously acquired anatomical images such as CT and MRI from hybrid scanners are also important ingredients for improving the image quality of PET or SPECT further. High-quality anatomical information has been used and investigated for attenuation and scatter corrections, motion compensation, and noise reduction via post-reconstruction filtering and regularization in inverse problems. In this article, we will review works using anatomical information for molecular image reconstruction algorithms for better image quality by describing mathematical models, discussing sources of anatomical information for different cases, and showing some examples.

Innovations in Small-Animal PET/MR Imaging Instrumentation

Multimodal imaging has led to a more detailed exploration of different physiologic processes with integrated PET/MR imaging being the most recent entry. Although the clinical need is still questioned, it is well recognized that it represents one of the most active and promising fields of medical imaging research in terms of software and hardware. The hardware developments have moved from small detector components to high-performance PET inserts and new concepts in full systems. Conversely, the software focuses on the efficient performance of necessary corrections without the use of CT data. The most recent developments in both directions are reviewed.

Direct Parametric Reconstruction Using Anatomical Regularization for Simultaneous PET/MRI Data

Pharmacokinetic analysis of dynamic positron emission tomography (PET) imaging data maps the measured time activity curves to a set of model-specific pharmacokinetic parameters. Voxel-based parameter estimation via curve fitting is conventionally performed indirectly on a sequence of independently reconstructed PET images, leading to high variance and bias in the parametric images. We propose a direct parametric reconstruction algorithm with raw projection data as input that leverages high-resolution anatomical information simultaneously obtained from magnetic resonance (MR) imaging in a PET/MRI scanner for regularization. The reconstruction problem is formulated in a flexible Bayesian framework with Gaussian Markov Random field modeling of activity, parameters, or both simultaneously. MR information is incorporated through a Bowsher-like prior function. Optimization transfer using an expectation-maximization surrogate and a new Bowsher-like penalty surrogate is applied to obtain a voxel-separable algorithm that interleaves a reconstruction with a fitting step. An analytical input function model is used. The algorithm is evaluated on simulated [(18)F]FDG and clinical [(18)F]FET brain data acquired with a Biograph mMR. The results indicate that direct and simultaneously regularized parametric reconstruction increases image quality. Anatomical regularization leads to higher contrast than conventional distance-weighted regularization.

Quantitative comparison of OSEM and penalized likelihood image reconstruction using relative difference penalties for clinical PET

Ordered subset expectation maximization (OSEM) is the most widely used algorithm for clinical PET image reconstruction. OSEM is usually stopped early and post-filtered to control image noise and does not necessarily achieve optimal quantitation accuracy. As an alternative to OSEM, we have recently implemented a penalized likelihood (PL) image reconstruction algorithm for clinical PET using the relative difference penalty with the aim of improving quantitation accuracy without compromising visual image quality. Preliminary clinical studies have demonstrated visual image quality including lesion conspicuity in images reconstructed by the PL algorithm is better than or at least as good as that in OSEM images. In this paper we evaluate lesion quantitation accuracy of the PL algorithm with the relative difference penalty compared to OSEM by using various data sets including phantom data acquired with an anthropomorphic torso phantom, an extended oval phantom and the NEMA image quality phantom; clinical data; and hybrid clinical data generated by adding simulated lesion data to clinical data. We focus on mean standardized uptake values and compare them for PL and OSEM using both time-of-flight (TOF) and non-TOF data. The results demonstrate improvements of PL in lesion quantitation accuracy compared to OSEM with a particular improvement in cold background regions such as lungs.

4D PET iterative deconvolution with spatiotemporal regularization for quantitative dynamic PET imaging

Quantitative measurements in dynamic PET imaging are usually limited by the poor counting statistics particularly in short dynamic frames and by the low spatial resolution of the detection system, resulting in partial volume effects (PVEs). In this work, we present a fast and easy to implement method for the restoration of dynamic PET images that have suffered from both PVE and noise degradation. It is based on a weighted least squares iterative deconvolution approach of the dynamic PET image with spatial and temporal regularization. Using simulated dynamic [(11)C] Raclopride PET data with controlled biological variations in the striata between scans, we showed that the restoration method provides images which exhibit less noise and better contrast between emitting structures than the original images. In addition, the method is able to recover the true time activity curve in the striata region with an error below 3% while it was underestimated by more than 20% without correction. As a result, the method improves the accuracy and reduces the variability of the kinetic parameter estimates calculated from the corrected images. More importantly it increases the accuracy (from less than 66% to more than 95%) of measured biological variations as well as their statistical detectivity.

Anatomy-guided brain PET imaging incorporating a joint prior model

We proposed a maximum a posterior (MAP) framework for incorporating information from co-registered anatomical images into PET image reconstruction through a novel anato-functional joint prior. The characteristic of the utilized hyperbolic potential function is determinate by the voxel intensity differences within the anatomical image, while the penalization is computed based on voxel intensity differences in reconstructed PET images. Using realistic simulated (18)FDG PET scan data, we optimized the performance of the proposed MAP reconstruction with the joint prior (JP-MAP) and compared its performance with conventional 3D MLEM and 3D MAP reconstructions. The proposed JP-MAP reconstruction algorithm resulted in quantitatively enhanced reconstructed images, as demonstrated in extensive FDG PET simulation study. The proposed method was also tested on a 20 min Florbetapir patient study performed on the high-resolution research tomograph. It was shown to outperform conventional methods in visual as well as quantitative accuracy assessment (in terms of regional noise versus activity value performance). The JP-MAP method was also compared with another MR-guided MAP reconstruction method, utilizing the Bowsher prior and was seen to result in some quantitative enhancements, especially in the case of MR-PET mis-registrations, and a definitive improvement in computational performance.

Time-of-flight PET image reconstruction using origin ensembles

The origin ensemble (OE) algorithm is a novel statistical method for minimum-mean-square-error (MMSE) reconstruction of emission tomography data. This method allows one to perform reconstruction entirely in the image domain, i.e. without the use of forward and backprojection operations. We have investigated the OE algorithm in the context of list-mode (LM) time-of-flight (TOF) PET reconstruction. In this paper, we provide a general introduction to MMSE reconstruction, and a statistically rigorous derivation of the OE algorithm. We show how to efficiently incorporate TOF information into the reconstruction process, and how to correct for random coincidences and scattered events. To examine the feasibility of LM-TOF MMSE reconstruction with the OE algorithm, we applied MMSE-OE and standard maximum-likelihood expectation-maximization (ML-EM) reconstruction to LM-TOF phantom data with a count number typically registered in clinical PET examinations. We analyzed the convergence behavior of the OE algorithm, and compared reconstruction time and image quality to that of the EM algorithm. In summary, during the reconstruction process, MMSE-OE contrast recovery (CRV) remained approximately the same, while background variability (BV) gradually decreased with an increasing number of OE iterations. The final MMSE-OE images exhibited lower BV and a slightly lower CRV than the corresponding ML-EM images. The reconstruction time of the OE algorithm was approximately 1.3 times longer. At the same time, the OE algorithm can inherently provide a comprehensive statistical characterization of the acquired data. This characterization can be utilized for further data processing, e.g. in kinetic analysis and image registration, making the OE algorithm a promising approach in a variety of applications.

PET-MRI: a review of challenges and solutions in the development of integrated multimodality imaging

The integration of positron emission tomography (PET) and magnetic resonance imaging (MRI) has been an ongoing research topic for the last 20 years. This paper gives an overview of the different developments and the technical problems associated with combining PET and MRI in one system. After explaining the different detector concepts for integrating PET-MRI and minimising interference the limitations and advantages of different solutions for the detector and system are described for preclinical and clinical imaging systems. The different integrated PET-MRI systems are described in detail. Besides detector concepts and system integration the challenges and proposed solutions for attenuation correction and the potential for motion correction and resolution recovery are also discussed in this topical review.

Sparse representation and dictionary learning penalized image reconstruction for positron emission tomography

Accurate and robust reconstruction of the radioactivity concentration is of great importance in positron emission tomography (PET) imaging. Given the Poisson nature of photo-counting measurements, we present a reconstruction framework that integrates sparsity penalty on a dictionary into a maximum likelihood estimator. Patch-sparsity on a dictionary provides the regularization for our effort, and iterative procedures are used to solve the maximum likelihood function formulated on Poisson statistics. Specifically, in our formulation, a dictionary could be trained on CT images, to provide intrinsic anatomical structures for the reconstructed images, or adaptively learned from the noisy measurements of PET. Accuracy of the strategy with very promising application results from Monte-Carlo simulations, and real data are demonstrated.

PET image reconstruction using kernel method

Image reconstruction from low-count positron emission tomography (PET) projection data is challenging because the inverse problem is ill-posed. Prior information can be used to improve image quality. Inspired by the kernel methods in machine learning, this paper proposes a kernel based method that models PET image intensity in each pixel as a function of a set of features obtained from prior information. The kernel-based image model is incorporated into the forward model of PET projection data and the coefficients can be readily estimated by the maximum likelihood (ML) or penalized likelihood image reconstruction. A kernelized expectation-maximization algorithm is presented to obtain the ML estimate. Computer simulations show that the proposed approach can achieve better bias versus variance trade-off and higher contrast recovery for dynamic PET image reconstruction than the conventional maximum likelihood method with and without post-reconstruction denoising. Compared with other regularization-based methods, the kernel method is easier to implement and provides better image quality for low-count data. Application of the proposed kernel method to a 4-D dynamic PET patient dataset showed promising results.

Detail-Preserving PET Reconstruction with Sparse Image Representation and Anatomical Priors

Positron emission tomography (PET) reconstruction is an ill-posed inverse problem which typically involves fitting a high-dimensional forward model of the imaging process to noisy, and sometimes undersampled photon emission data. To improve the image quality, prior information derived from anatomical images of the same subject has been previously used in the penalised maximum likelihood (PML) method to regularise the model complexity and selectively smooth the image on a voxel basis in PET reconstruction. In this work, we propose a novel perspective of incorporating the prior information by exploring the sparse property of natural images. Instead of a regular voxel grid, the sparse image representation jointly determined by the prior image and the PET data is used in reconstruction to leverage between the image details and smoothness, and this prior is integrated into the PET forward model and has a closed-form expectation maximisation (EM) solution. Simulations show that the proposed approach achieves improved bias versus variance trade-off and higher contrast recovery than the current state-of-the-art methods, and preserves the image details better. Application to clinical PET data shows promising results.

Anatomy assisted PET image reconstruction incorporating multi-resolution joint entropy

A promising approach in PET image reconstruction is to incorporate high resolution anatomical information (measured from MR or CT) taking the anato-functional similarity measures such as mutual information or joint entropy (JE) as the prior. These similarity measures only classify voxels based on intensity values, while neglecting structural spatial information. In this work, we developed an anatomy-assisted maximum a posteriori (MAP) reconstruction algorithm wherein the JE measure is supplied by spatial information generated using wavelet multi-resolution analysis. The proposed wavelet-based JE (WJE) MAP algorithm involves calculation of derivatives of the subband JE measures with respect to individual PET image voxel intensities, which we have shown can be computed very similarly to how the inverse wavelet transform is implemented. We performed a simulation study with the BrainWeb phantom creating PET data corresponding to different noise levels. Realistically simulated T1-weighted MR images provided by BrainWeb modeling were applied in the anatomy-assisted reconstruction with the WJE-MAP algorithm and the intensity-only JE-MAP algorithm. Quantitative analysis showed that the WJE-MAP algorithm performed similarly to the JE-MAP algorithm at low noise level in the gray matter (GM) and white matter (WM) regions in terms of noise versus bias tradeoff. When noise increased to medium level in the simulated data, the WJE-MAP algorithm started to surpass the JE-MAP algorithm in the GM region, which is less uniform with smaller isolated structures compared to the WM region. In the high noise level simulation, the WJE-MAP algorithm presented clear improvement over the JE-MAP algorithm in both the GM and WM regions. In addition to the simulation study, we applied the reconstruction algorithms to real patient studies involving DPA-173 PET data and Florbetapir PET data with corresponding T1-MPRAGE MRI images. Compared to the intensity-only JE-MAP algorithm, the WJE-MAP algorithm resulted in comparable regional mean values to those from the maximum likelihood algorithm while reducing noise. Achieving robust performance in various noise-level simulation and patient studies, the WJE-MAP algorithm demonstrates its potential in clinical quantitative PET imaging.

Unconstrained image reconstruction with resolution modelling does not have a unique solution

Positron emission tomography systems have a finite spatial resolution. When the system point spread function (PSF) is taken into account, the unconstrained reconstruction problem does not have a unique solution. As a result, the solution obtained with the maximum likelihood reconstruction algorithm typically suffers from Gibbs artefacts, which can have an adverse effect on tracer uptake quantification in small lesions. To deal with this problem, some assumptions about the undetected image features have to be introduced, either implicitly or explicitly. If one is willing to sacrifice resolution, the improvement of the PSF model can be used to suppress noise and at the same time impose a predefined (suboptimal) spatial resolution, facilitating pooled analysis of multicentre data.

Alternating direction method of multiplier for tomography with nonlocal regularizers

The ordered subset expectation maximization (OSEM) algorithm approximates the gradient of a likelihood function using a subset of projections instead of using all projections so that fast image reconstruction is possible for emission and transmission tomography such as SPECT, PET, and CT. However, OSEM does not significantly accelerate reconstruction with computationally expensive regularizers such as patch-based nonlocal (NL) regularizers, because the regularizer gradient is evaluated for every subset. We propose to use variable splitting to separate the likelihood term and the regularizer term for penalized emission tomographic image reconstruction problem and to optimize it using the alternating direction method of multiplier (ADMM). We also propose a fast algorithm to optimize the ADMM parameter based on convergence rate analysis. This new scheme enables more sub-iterations related to the likelihood term. We evaluated our ADMM for 3-D SPECT image reconstruction with a patch-based NL regularizer that uses the Fair potential function. Our proposed ADMM improved the speed of convergence substantially compared to other existing methods such as gradient descent, EM, and OSEM using De Pierro's approach, and the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm.

Fat-constrained 18F-FDG PET reconstruction in hybrid PET/MR imaging

Fusion of information from PET and MR imaging can increase the diagnostic value of both modalities. This work sought to improve (18)F FDG PET image quality by using MR Dixon fat-constrained images to constrain PET image reconstruction to low-fat regions, with the working hypothesis that fatty tissue metabolism is low in glucose consumption.

METHODS

A novel constrained PET reconstruction algorithm was implemented via a modification of the system matrix in list-mode time-of-flight ordered-subsets expectation maximization reconstruction, similar to the way time-of-flight weighting is incorporated. To demonstrate its use in PET/MR imaging, we modeled a constraint based on fat/water-separating Dixon MR images that shift activity away from regions of fat tissue during PET image reconstruction. PET and MR imaging scans of a modified National Electrical Manufacturers Association/International Electrotechnical Commission body phantom simulating body fat/water composition and in vivo experiments on 2 oncology patients were performed on a commercial time-of-flight PET/MR imaging system.

RESULTS

Fat-constrained PET reconstruction visibly and quantitatively increased resolution and contrast between high-uptake and fatty-tissue regions without significantly affecting the images in nonfat regions.

CONCLUSION

The incorporation of MR tissue information, such as fat, in image reconstruction can improve the quality of PET images. The combination of a variety of potential other MR tissue characteristics with PET represents a further justification for merging MR data with PET data in hybrid systems.

Voxel-based comparison of state-of-the-art reconstruction algorithms for 18F-FDG PET brain imaging using simulated and clinical data

The resolution of a PET scanner (2.5-4.5mm for brain imaging) is similar to the thickness of the cortex in the (human) brain (2.5mm on average), hampering accurate activity distribution reconstruction. Many techniques to compensate for the limited resolution during or post-reconstruction have been proposed in the past and have been shown to improve the quantitative accuracy. In this study, state-of-the-art reconstruction techniques are compared on a voxel-basis for quantification accuracy and group analysis using both simulated and measured data of healthy volunteers and patients with epilepsy.

METHODS

Maximum a posteriori (MAP) reconstructions using either a segmentation-based or a segmentation-less anatomical prior were compared to maximum likelihood expectation maximization (MLEM) reconstruction with resolution recovery. As anatomical information, a spatially aligned 3D T1-weighted magnetic resonance image was used. Firstly, the algorithms were compared using normal brain images to detect systematic bias with respect to the true activity distribution, as well as systematic differences between two methods. Secondly, it was verified whether the algorithms yielded similar results in a group comparison study.

RESULTS

Significant differences were observed between the reconstructed and the true activity, with the largest errors when using (post-smoothed) MLEM. Only 5-10% underestimation in cortical gray matter voxel activity was found for both MAP reconstructions. Higher errors were observed at GM edges. MAP with the segmentation-based prior also resulted in a significant bias in the subcortical regions due to segmentation inaccuracies, while MAP with the anatomical prior which does not need segmentation did not. Significant differences in reconstructed activity were also found between the algorithms at similar locations (mainly in gray matter edge voxels and in cerebrospinal fluid voxels) in the simulated as well as in the clinical data sets. Nevertheless, when comparing two groups, very similar regions of significant hypometabolism were detected by all algorithms.

CONCLUSION

Including anatomical a priori information during reconstruction in combination with resolution modeling yielded accurate gray matter activity estimates, and a significant improvement in quantification accuracy was found when compared to post-smoothed MLEM reconstruction with resolution modeling. AsymBowsher provided the most accurate subcortical GM activity estimates. It is also reassuring that the differences found between the algorithms did not hamper the detection of hypometabolic regions in the gray matter when performing a voxel-based group comparison. Nevertheless, the size of the detected clusters differed. More elaborated and application-specific studies are required to decide which algorithm is best for a group analysis.

Post-reconstruction non-local means filtering methods using CT side information for quantitative SPECT

Quantitative SPECT techniques are important for many applications including internal emitter therapy dosimetry where accurate estimation of total target activity and activity distribution within targets are both potentially important for dose–response evaluations. We investigated non-local means (NLM) post-reconstruction filtering for accurate I-131 SPECT estimation of both total target activity and the 3D activity distribution. We first investigated activity estimation versus number of ordered-subsets expectation–maximization (OSEM) iterations. We performed simulations using the XCAT phantom with tumors containing a uniform and a non-uniform activity distribution, and measured the recovery coefficient (RC) and the root mean squared error (RMSE) to quantify total target activity and activity distribution, respectively. We observed that using more OSEM iterations is essential for accurate estimation of RC, but may or may not improve RMSE. We then investigated various post-reconstruction filtering methods to suppress noise at high iteration while preserving image details so that both RC and RMSE can be improved. Recently, NLM filtering methods have shown promising results for noise reduction. Moreover, NLM methods using high-quality side information can improve image quality further. We investigated several NLM methods with and without CT side information for I-131 SPECT imaging and compared them to conventional Gaussian filtering and to unfiltered methods. We studied four different ways of incorporating CT information in the NLM methods: two known (NLM CT-B and NLM CT-M) and two newly considered (NLM CT-S and NLM CT-H). We also evaluated the robustness of NLM filtering using CT information to erroneous CT. NLM CT-S and NLM CT-H yielded comparable RC values to unfiltered images while substantially reducing RMSE. NLM CT-S achieved −2.7 to 2.6% increase of RC compared to no filtering and NLM CT-H yielded up to 6% decrease in RC while other methods yielded lower RCs than them: Gaussian filtering (up to 11.8% decrease in RC), NLM method without CT (up to 9.5% decrease in RC), and NLM CT-M and NLM CT-B (up to 19.4% decrease in RC). NLM CT-S and NLM CT-H achieved 8.2 to 33.9% and −0.9 to 36% decreased RMSE on tumors compared to no filtering respectively while other methods yielded less reduced or increased RMSE: Gaussian filtering (up to 7.9% increase in RMSE), NLM method without CT (up to 18.3% increase in RMSE), and NLM CT-M and NLM CT-B (up to 31.5% increase in RMSE). NLM CT-S and NLM CT-H also yielded images with tumor shapes that better-matched the true shapes than other methods. All NLM methods using CT information were robust to small misregistration between SPECT and CT, but NLM CT-S and NLM CT-H were more sensitive than NLM CT-M and NLM CT-B to missing CT information.

Postreconstruction nonlocal means filtering of whole-body PET with an anatomical prior

Positron emission tomography (PET) images usually suffer from poor signal-to-noise ratio (SNR) due to the high level of noise and low spatial resolution, which adversely affect its performance for lesion detection and quantification. The complementary information present in high-resolution anatomical images from multi-modality imaging systems could potentially be used to improve the ability to detect and/or quantify lesions. However, previous methods that use anatomical priors usually require matched organ/lesion boundaries. In this study, we investigated the use of anatomical information to suppress noise in PET images while preserving both quantitative accuracy and the amplitude of prominent signals that do not have corresponding boundaries on computerized tomography (CT). The proposed approach was realized through a postreconstruction filter based on the nonlocal means (NLM) filter, which reduces noise by computing the weighted average of voxels based on the similarity measurement between patches of voxels within the image. Anatomical knowledge obtained from CT was incorporated to constrain the similarity measurement within a subset of voxels. In contrast to other methods that use anatomical priors, the actual number of neighboring voxels and weights used for smoothing were determined from a robust measurement on PET images within the subset. Thus, the proposed approach can be robust to signal mismatches between PET and CT. A 3-D search scheme was also investigated for the volumetric PET/CT data. The proposed anatomically guided median nonlocal means filter (AMNLM) was first evaluated using a computer phantom and a physical phantom to simulate realistic but challenging situations where small lesions are located in homogeneous regions, which can be detected on PET but not on CT. The proposed method was further assessed with a clinical study of a patient with lung lesions. The performance of the proposed method was compared to Gaussian, edge-preserving bilateral and NLM filters, as well as median nonlocal means (MNLM) filtering without an anatomical prior. The proposed AMNLM method yielded improved lesion contrast and SNR compared with other methods even with imperfect anatomical knowledge, such as missing lesion boundaries and mismatched organ boundaries.

Dynamic positron emission tomography image restoration via a kinetics-induced bilateral filter

Dynamic positron emission tomography (PET) imaging is a powerful tool that provides useful quantitative information on physiological and biochemical processes. However, low signal-to-noise ratio in short dynamic frames makes accurate kinetic parameter estimation from noisy voxel-wise time activity curves (TAC) a challenging task. To address this problem, several spatial filters have been investigated to reduce the noise of each frame with noticeable gains. These filters include the Gaussian filter, bilateral filter, and wavelet-based filter. These filters usually consider only the local properties of each frame without exploring potential kinetic information from entire frames. Thus, in this work, to improve PET parametric imaging accuracy, we present a kinetics-induced bilateral filter (KIBF) to reduce the noise of dynamic image frames by incorporating the similarity between the voxel-wise TACs using the framework of bilateral filter. The aim of the proposed KIBF algorithm is to reduce the noise in homogeneous areas while preserving the distinct kinetics of regions of interest. Experimental results on digital brain phantom and in vivo rat study with typical ¹⁸F-FDG kinetics have shown that the present KIBF algorithm can achieve notable gains over other existing algorithms in terms of quantitative accuracy measures and visual inspection.

Incorporating anatomical side information into PET reconstruction using nonlocal regularization

With the introduction of combined positron emission tomography (PET)/computed tomography (CT) or PET/magnetic resonance imaging (MRI) scanners, there is an increasing emphasis on reconstructing PET images with the aid of the anatomical side information obtained from X-ray CT or MRI scanners. In this paper, we propose a new approach to incorporating prior anatomical information into PET reconstruction using the nonlocal regularization method. The nonlocal regularizer developed for this application is designed to selectively consider the anatomical information only when it is reliable. As our proposed nonlocal regularization method does not directly use anatomical edges or boundaries which are often used in conventional methods, it is not only free from additional processes to extract anatomical boundaries or segmented regions, but also more robust to the signal mismatch problem that is caused by the indirect relationship between the PET image and the anatomical image. We perform simulations with digital phantoms. According to our experimental results, compared to the conventional method based on the traditional local regularization method, our nonlocal regularization method performs well even with the imperfect prior anatomical information or in the presence of signal mismatch between the PET image and the anatomical image.

Magnetic resonance-guided positron emission tomography image reconstruction

The resolution of positron emission tomography (PET) images is limited by the physics of positron-electron annihilation and instrumentation for photon coincidence detection. Model-based methods that incorporate accurate physical and statistical models have produced significant improvements in reconstructed image quality when compared with filtered backprojection reconstruction methods. However, it has often been suggested that by incorporating anatomical information, the resolution and noise properties of PET images could be further improved, leading to better quantitation or lesion detection. With the recent development of combined MR-PET scanners, we can now collect intrinsically coregistered magnetic resonance images. It is therefore possible to routinely make use of anatomical information in PET reconstruction, provided appropriate methods are available. In this article, we review research efforts over the past 20 years to develop these methods. We discuss approaches based on the use of both Markov random field priors and joint information or entropy measures. The general framework for these methods is described, and their performance and longer-term potential and limitations are discussed.

3.5D dynamic PET image reconstruction incorporating kinetics-based clusters

Standard 3D dynamic positron emission tomographic (PET) imaging consists of independent image reconstructions of individual frames followed by application of appropriate kinetic model to the time activity curves at the voxel or region-of-interest (ROI). The emerging field of 4D PET reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple frames within the image reconstruction task. Here we propose a novel reconstruction framework aiming to enhance quantitative accuracy of parametric images via introduction of priors based on voxel kinetics, as generated via clustering of preliminary reconstructed dynamic images to define clustered neighborhoods of voxels with similar kinetics. This is then followed by straightforward maximum a posteriori (MAP) 3D PET reconstruction as applied to individual frames; and as such the method is labeled '3.5D' image reconstruction. The use of cluster-based priors has the advantage of further enhancing quantitative performance in dynamic PET imaging, because: (a) there are typically more voxels in clusters than in conventional local neighborhoods, and (b) neighboring voxels with distinct kinetics are less likely to be clustered together. Using realistic simulated (11)C-raclopride dynamic PET data, the quantitative performance of the proposed method was investigated. Parametric distribution-volume (DV) and DV ratio (DVR) images were estimated from dynamic image reconstructions using (a) maximum-likelihood expectation maximization (MLEM), and MAP reconstructions using (b) the quadratic prior (QP-MAP), (c) the Green prior (GP-MAP) and (d, e) two proposed cluster-based priors (CP-U-MAP and CP-W-MAP), followed by graphical modeling, and were qualitatively and quantitatively compared for 11 ROIs. Overall, the proposed dynamic PET reconstruction methodology resulted in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) for parametric DV and DVR images. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomography. The proposed method was shown to outperform the conventional method in visual as well as quantitative accuracy improvements (in terms of noise versus regional DVR value performance).