Noise properties of motion-compensated tomographic image reconstruction methods

Joint estimation of activity, attenuation and motion in respiratory-self-gated time-of-flight PET

Objective. Whole-body positron emission tomography (PET) imaging is often hindered by respiratory motion during acquisition, causing significant degradation in the quality of reconstructed activity images. An additional challenge in PET/CT imaging arises from the respiratory phase mismatch between CT-based attenuation correction and PET acquisition, leading to attenuation artifacts. To address these issues, we propose two new, purely data-driven methods for the joint estimation of activity, attenuation, and motion in respiratory self-gated time-of-flight PET. These methods enable the reconstruction of a single activity image free from motion and attenuation artifacts.Approach. The proposed methods were evaluated using data from the anthropomorphic Wilhelm phantom acquired on a Siemens mCT PET/CT system, as well as three clinical [18F]FDG PET/CT datasets acquired on a GE DMI PET/CT system. Image quality was assessed visually to identify motion and attenuation artifacts. Lesion uptake values were quantitatively compared across reconstructions without motion modeling, with motion modeling but 'static' attenuation correction, and with our proposed methods.Main results. For the Wilhelm phantom, the proposed methods delivered image quality closely matching the reference reconstruction from a static acquisition. The lesion-to-background contrast for a liver dome lesion improved from 2.0 (no motion correction) to 5.2 (using our proposed methods), matching the contrast from the static acquisition (5.2). In contrast, motion modeling with 'static' attenuation correction yielded a lower contrast of 3.5. In patient datasets, the proposed methods successfully reduced motion artifacts in lung and liver lesions and mitigated attenuation artifacts, demonstrating superior lesion to background separation.Significance. Our proposed methods enable the reconstruction of a single, high-quality activity image that is motion-corrected and free from attenuation artifacts, without the need for external hardware.

Joint estimation of activity, attenuation and motion in respiratory-self-gated time-of-flight PET

Whole-body PET imaging is often hindered by respiratory motion during acquisition, causing significant degradation in the quality of reconstructed activity images. An additional challenge in PET/CT imaging arises from the respiratory phase mismatch between CT-based attenuation correction and PET acquisition, leading to attenuation artifacts. To address these issues, we propose two new, purely data-driven methods for the joint estimation of activity, attenuation, and motion in respiratory self-gated TOF PET. These methods enable the reconstruction of a single activity image free from motion and attenuation artifacts. The proposed methods were evaluated using data from the anthropomorphic Wilhelm phantom acquired on a Siemens mCT PET/CT system, as well as 3 clinical FDG PET/CT datasets acquired on a GE DMI PET/CT system. Image quality was assessed visually to identify motion and attenuation artifacts. Lesion uptake values were quantitatively compared across reconstructions without motion modeling, with motion modeling but static attenuation correction, and with our proposed methods. For the Wilhelm phantom, the proposed methods delivered image quality closely matching the reference reconstruction from a static acquisition. The lesion-to-background contrast for a liver dome lesion improved from 2.0 (no motion correction) to 5.2 (proposed methods), matching the contrast from the static acquisition (5.2). In contrast, motion modeling with static attenuation correction yielded a lower contrast of 3.5. In patient datasets, the proposed methods successfully reduced motion artifacts in lung and liver lesions and mitigated attenuation artifacts, demonstrating superior lesion to background separation. Our proposed methods enable the reconstruction of a single, high-quality activity image that is motion-corrected and free from attenuation artifacts, without the need for external hardware.

PET respiratory motion correction: quo vadis?

Positron emission tomography (PET) respiratory motion correction has been a subject of great interest for the last twenty years, prompted mainly by the development of multimodality imaging devices such as PET/computed tomography (CT) and PET/magnetic resonance imaging (MRI). PET respiratory motion correction involves a number of steps including acquisition synchronization, motion estimation and finally motion correction. The synchronization steps include the use of different external device systems or data driven approaches which have been gaining ground over the last few years. Patient specific or generic motion models using the respiratory synchronized datasets can be subsequently derived and used for correction either in the image space or within the image reconstruction process. Similar overall approaches can be considered and have been proposed for both PET/CT and PET/MRI devices. Certain variations in the case of PET/MRI include the use of MRI specific sequences for the registration of respiratory motion information. The proposed review includes a comprehensive coverage of all these areas of development in field of PET respiratory motion for different multimodality imaging devices and approaches in terms of synchronization, estimation and subsequent motion correction. Finally, a section on perspectives including the potential clinical usage of these approaches is included.

General simultaneous motion estimation and image reconstruction (G-SMEIR)

To achieve better performance for 4D multi-frame reconstruction with the parametric motion model (MF-PMM), a general simultaneous motion estimation and image reconstruction (G-SMEIR) method is proposed. In G-SMEIR, projection domain motion estimation and image domain motion estimation are performed alternatively to achieve better 4D reconstruction. This method can mitigate the local optimum trapping problem in either domain. To improve computational efficiency, the image domain motion estimation is accelerated by adapting fast convergent algorithms and graphics processing unit (GPU) computing. The proposed G-SMEIR method is tested using a cone-beam computed tomography (CBCT) simulation study of 4D XCAT phantom at different dose levels and compared with 3D total variation-based reconstruction (3D TV), 4D reconstruction with image domain motion estimation (IM4D), and SMEIR. G-SMEIR shows strong denoising capability and achieves similar performance at regular dose and half dose. The root mean squared error (RMSE) of G-SMEIR is the best among the four methods and improved about 12% over SMEIR for all respiratory phase images at full dose. G-SMEIR also achieved the best structural similarity index (SSIM) values among all methods. More importantly, G-SMEIR leads to more than 40% improvement of the mean deviation from the phantom tumor motion over SMEIR. A preliminary patient CBCT image reconstruction also shows better image quality of G-SMEIR than that of the frame-by-frame reconstruction (3D TV) and MF-PMM either using image domain motion estimation (IM4D) or using projection domain motion estimation (SMEIR) alone. G-SMEIR with a flexible combination of image domain and projection domain motion estimation provides an effective tool for 4D tomographic reconstruction.

Enhancing Cardiac PET by Motion Correction Techniques

PURPOSE OF REVIEW

Cardiac positron emission tomography (PET) images often contain errors due to cardiac, respiratory, and patient motion during relatively long image acquisition. Advanced motion compensation techniques may improve PET spatial resolution, eliminate potential artifacts, and ultimately improve the research and clinical capabilities of PET.

RECENT FINDINGS

Combined cardiac and respiratory gating has only recently been implemented in clinical PET systems. Considering that the gated image bins contain much lower counts than the original PET data, they need to be summed after correcting for motion, forming motion-corrected, high-count image volume. Furthermore, automated image registration techniques can be used to correct for motion between CT attenuation scan and PET acquisition. While motion correction methods are not yet widely used in clinical practice, approaches including dual-gated non-rigid motion correction and the incorporation of motion correction information into the reconstruction process have the potential to markedly improve cardiac PET imaging.

Enhancing ejection fraction measurement through 4D respiratory motion compensation in cardiac PET imaging

ECG gated cardiac PET imaging measures functional parameters such as left ventricle (LV) ejection fraction (EF), providing diagnostic and prognostic information for management of patients with coronary artery disease (CAD). Respiratory motion degrades spatial resolution and affects the accuracy in measuring the LV volumes for EF calculation. The goal of this study is to systematically investigate the effect of respiratory motion correction on the estimation of end-diastolic volume (EDV), end-systolic volume (ESV), and EF, especially on the separation of normal and abnormal EFs. We developed a respiratory motion incorporated 4D PET image reconstruction technique which uses all gated-frame data to acquire a motion-suppressed image. Using the standard XCAT phantom and two individual-specific volunteer XCAT phantoms, we simulated dual-gated myocardial perfusion imaging data for normally and abnormally beating hearts. With and without respiratory motion correction, we measured the EDV, ESV, and EF from the cardiac-gated reconstructed images. For all the phantoms, the estimated volumes increased and the biases significantly reduced with motion correction compared with those without. Furthermore, the improvement of ESV measurement in the abnormally beating heart led to better separation of normal and abnormal EFs. The simulation study demonstrated the significant effect of respiratory motion correction on cardiac imaging data with motion amplitude as small as 0.7 cm. The larger the motion amplitude the more improvement respiratory motion correction brought about on the EF measurement. Using data-driven respiratory gating, we also demonstrated the effect of respiratory motion correction on estimating the above functional parameters from list mode patient data. Respiratory motion correction has been shown to improve the accuracy of EF measurement in clinical cardiac PET imaging.

Pulmonary imaging using respiratory motion compensated simultaneous PET/MR

PURPOSE

Pulmonary positron emission tomography (PET) imaging is confounded by blurring artifacts caused by respiratory motion. These artifacts degrade both image quality and quantitative accuracy. In this paper, the authors present a complete data acquisition and processing framework for respiratory motion compensated image reconstruction (MCIR) using simultaneous whole body PET/magnetic resonance (MR) and validate it through simulation and clinical patient studies.

METHODS

The authors have developed an MCIR framework based on maximum a posteriori or MAP estimation. For fast acquisition of high quality 4D MR images, the authors developed a novel Golden-angle RAdial Navigated Gradient Echo (GRANGE) pulse sequence and used it in conjunction with sparsity-enforcing k-t FOCUSS reconstruction. The authors use a 1D slice-projection navigator signal encapsulated within this pulse sequence along with a histogram-based gate assignment technique to retrospectively sort the MR and PET data into individual gates. The authors compute deformation fields for each gate via nonrigid registration. The deformation fields are incorporated into the PET data model as well as utilized for generating dynamic attenuation maps. The framework was validated using simulation studies on the 4D XCAT phantom and three clinical patient studies that were performed on the Biograph mMR, a simultaneous whole body PET/MR scanner.

RESULTS

The authors compared MCIR (MC) results with ungated (UG) and one-gate (OG) reconstruction results. The XCAT study revealed contrast-to-noise ratio (CNR) improvements for MC relative to UG in the range of 21%-107% for 14 mm diameter lung lesions and 39%-120% for 10 mm diameter lung lesions. A strategy for regularization parameter selection was proposed, validated using XCAT simulations, and applied to the clinical studies. The authors' results show that the MC image yields 19%-190% increase in the CNR of high-intensity features of interest affected by respiratory motion relative to UG and a 6%-51% increase relative to OG.

CONCLUSIONS

Standalone MR is not the traditional choice for lung scans due to the low proton density, high magnetic susceptibility, and low T2 (∗) relaxation time in the lungs. By developing and validating this PET/MR pulmonary imaging framework, the authors show that simultaneous PET/MR, unique in its capability of combining structural information from MR with functional information from PET, shows promise in pulmonary imaging.

Motion correction options in PET/MRI

Subject motion is unavoidable in clinical and research imaging studies. Breathing is the most important source of motion in whole-body PET and MRI studies, affecting not only thoracic organs but also those in the upper and even lower abdomen. The motion related to the pumping action of the heart is obviously relevant in high-resolution cardiac studies. These two sources of motion are periodic and predictable, at least to a first approximation, which means certain techniques can be used to control the motion (eg, by acquiring the data when the organ of interest is relatively at rest). Additionally, nonperiodic and unpredictable motion can also occur during the scan. One obvious limitation of methods relying on external devices (eg, respiratory bellows or the electrocardiogram signal to monitor the respiratory or cardiac cycle, respectively) to trigger or gate the data acquisition is that the complex motion of internal organs cannot be fully characterized. However, detailed information can be obtained using either the PET or MRI data (or both) allowing the more complete characterization of the motion field so that a motion model can be built. Such a model and the information derived from simple external devices can be used to minimize the effects of motion on the collected data. In the ideal case, all the events recorded during the PET scan would be used to generate a motion-free or corrected PET image. The detailed motion field can be used for this purpose by applying it to the PET data before, during, or after the image reconstruction. Integrating all these methods for motion control, characterization, and correction into a workflow that can be used for routine clinical studies is challenging but could potentially be extremely valuable given the improvement in image quality and reduction of motion-related image artifacts.

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.

Respiratory motion correction of PET using MR-constrained PET-PET registration

Background

Respiratory motion in positron emission tomography (PET) is an unavoidable source of error in the measurement of tracer uptake, lesion position and lesion size. The introduction of PET-MR dual modality scanners opens a new avenue for addressing this issue. Motion models offer a way to estimate motion using a reduced number of parameters. This can be beneficial for estimating motion from PET, which can otherwise be difficult due to the high level of noise of the data.

Method

We propose a novel technique that makes use of a respiratory motion model, formed from initial MR scan data. The motion model is used to constrain PET-PET registrations between a reference PET gate and the gates to be corrected. For evaluation, PET with added FDG-avid lesions was simulated from real, segmented, ultrashort echo time MR data obtained from four volunteers. Respiratory motion was included in the simulations using motion fields derived from real dynamic 3D MR volumes obtained from the same volunteers.

Results

Performance was compared to an MR-derived motion model driven method (which requires constant use of the MR scanner) and to unconstrained PET-PET registration of the PET gates. Without motion correction, a median drop in uncorrected lesion \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm {SUV}}_{\mathrm {peak}}$$\end{document}SUVpeak intensity to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$78.4 \pm 18.6 \,\,\%$$\end{document}78.4±18.6% and an increase in median head-foot lesion width, specified by a minimum bounding box, to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$179 \pm 63.7\,\, \%$$\end{document}179±63.7% was observed relative to the corresponding measures in motion-free simulations. The proposed method corrected these values to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$86.9 \pm 13.6\,\, \%$$\end{document}86.9±13.6% (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p<0.001$$\end{document}p<0.001) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$100 \pm 29.12\,\, \%$$\end{document}100±29.12% (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p<0.001$$\end{document}p<0.001) respectively, with notably improved performance close to the diaphragm and in the liver. Median lesion displacement across all lesions was observed to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$6.6 \pm 5.4\,\mathrm {mm}$$\end{document}6.6±5.4mm without motion correction, which was reduced to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.5 \pm 1.8\,\mathrm {mm}$$\end{document}3.5±1.8mm (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p<0.001$$\end{document}p<0.001) with motion correction.

Discussion

This paper presents a novel technique for respiratory motion correction of PET data in PET-MR imaging. After an initial 30 second MR scan, the proposed technique does not require use of the MR scanner for motion correction purposes, making it suitable for MR-intensive studies or sequential PET-MR. The accuracy of the proposed technique was similar to both comparative methods, but robustness was improved compared to the PET-PET technique, particularly in regions with higher noise such as the liver.

Estimation of noise properties for TV-regularized image reconstruction in computed tomography

A method for predicting the image covariance resulting from total-variation-penalized iterative image reconstruction (TV-penalized IIR) is presented and demonstrated in a variety of contexts. The method is validated against the sample covariance from statistical noise realizations for a small image using a variety of comparison metrics. Potential applications for the covariance approximation include investigation of image properties such as object- and signal-dependence of noise, and noise stationarity. These applications are demonstrated, along with the construction of image pixel variance maps for two-dimensional 128 × 128 pixel images. Methods for extending the proposed covariance approximation to larger images and improving computational efficiency are discussed. Future work will apply the developed methodology to the construction of task-based image quality metrics such as the Hotelling observer detectability for TV-based IIR.

Relative role of motion and PSF compensation in whole-body oncologic PET-MR imaging

PURPOSE

Respiratory motion and partial-volume effects are the two main sources of image degradation in whole-body PET imaging. Simultaneous PET-MR allows measurement of respiratory motion using MRI while collecting PET events. Improved PET images may be obtained by modeling respiratory motion and point spread function (PSF) within the PET iterative reconstruction process. In this study, the authors assessed the relative impact of PSF modeling and MR-based respiratory motion correction in phantoms and patient studies using a whole-body PET-MR scanner.

METHODS

An asymmetric exponential PSF model accounting for radially varying and axial detector blurring effects was obtained from point source acquisitions performed in the PET-MR scanner. A dedicated MRI acquisition protocol using single-slice steady state free-precession MR acquisitions interleaved with pencil-beam navigator echoes was developed to track respiratory motion during PET-MR studies. An iterative ordinary Poisson fully 3D OSEM PET reconstruction algorithm modeling all the physical effects of the acquisition (attenuation, scatters, random events, detectors efficiencies, PSF), as well as MR-based nonrigid respiratory deformations of tissues (in both emission and attenuation maps) was developed. Phantom and(18)F-FDG PET-MR patient studies were performed to evaluate the proposed quantitative PET-MR methods.

RESULTS

The phantom experiment results showed that PSF modeling significantly improved contrast recovery while limiting noise propagation in the reconstruction process. In patients with soft-tissue static lesions, PSF modeling improved lesion contrast by 19.7%-109%, enhancing the detectability and assessment of small tumor foci. In a patient study with small moving hepatic lesions, the proposed reconstruction technique improved lesion contrast by 54.4%-98.1% and reduced apparent lesion size by 21.8%-34.2%. Improvements were particularly important for the smallest lesion undergoing large motion at the lung-liver interface. Heterogeneous tumor structures delineation was substantially improved. Enhancements offered by PSF modeling were more important when correcting for motion at the same time.

CONCLUSIONS

The results suggest that the proposed quantitative PET-MR methods can significantly enhance the performance of tumor diagnosis and staging as compared to conventional methods. This approach may enable utilization of the full potential of the scanner in oncologic studies of both the lower abdomen, with moving lesions, as well as other parts of the body unaffected by motion.

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.

Motion based X-ray imaging modality

A new X-ray imaging method (patent pending) was developed to visualize function-related motion information. We modify existing X-ray imaging methods to provide four images without increasing the necessary measurement time or radiation dose. The most important of these images is a new "kinetic" image that represents motions inside the object or living body. The motion-based contrast of the kinetic image can help visualize details that were not accessible before. The broad range of the movements and high sensitivity of the method are illustrated by imaging the mechanics of a working clock and the chest of a living African clawed frog (Xenopus laevis). The heart, valves, aorta, and lungs of the frog are clearly visualized in spite of the low soft tissue contrast of the animal. The new technology also reconstructs a "static" image similar to the existing conventional X-ray image. The static image shows practically the same information as the conventional image. The new technology presents two more images which show the point-wise errors of the static and kinetic images. This technique gives a better estimation of errors than present methods because it is based entirely on measured data. The new technology could be used in imaging cardiopulmonary movements, nondestructive testing, or port security screening.

Quantitative statistical methods for image quality assessment

Quantitative measures of image quality and reliability are critical for both qualitative interpretation and quantitative analysis of medical images. While, in theory, it is possible to analyze reconstructed images by means of Monte Carlo simulations using a large number of noise realizations, the associated computational burden makes this approach impractical. Additionally, this approach is less meaningful in clinical scenarios, where multiple noise realizations are generally unavailable. The practical alternative is to compute closed-form analytical expressions for image quality measures. The objective of this paper is to review statistical analysis techniques that enable us to compute two key metrics: resolution (determined from the local impulse response) and covariance. The underlying methods include fixed-point approaches, which compute these metrics at a fixed point (the unique and stable solution) independent of the iterative algorithm employed, and iteration-based approaches, which yield results that are dependent on the algorithm, initialization, and number of iterations. We also explore extensions of some of these methods to a range of special contexts, including dynamic and motion-compensated image reconstruction. While most of the discussed techniques were developed for emission tomography, the general methods are extensible to other imaging modalities as well. In addition to enabling image characterization, these analysis techniques allow us to control and enhance imaging system performance. We review practical applications where performance improvement is achieved by applying these ideas to the contexts of both hardware (optimizing scanner design) and image reconstruction (designing regularization functions that produce uniform resolution or maximize task-specific figures of merit).

List-mode reconstruction for the Biograph mCT with physics modeling and event-by-event motion correction

Whole-body PET/CT scanners are important clinical and research tools to study tracer distribution throughout the body. In whole-body studies, respiratory motion results in image artifacts. We have previously demonstrated for brain imaging that, when provided with accurate motion data, event-by-event correction has better accuracy than frame-based methods. Therefore, the goal of this work was to develop a list-mode reconstruction with novel physics modeling for the Siemens Biograph mCT with event-by-event motion correction, based on the MOLAR platform (Motion-compensation OSEM List-mode Algorithm for Resolution-Recovery Reconstruction). Application of MOLAR for the mCT required two algorithmic developments. First, in routine studies, the mCT collects list-mode data in 32 bit packets, where averaging of lines-of-response (LORs) by axial span and angular mashing reduced the number of LORs so that 32 bits are sufficient to address all sinogram bins. This degrades spatial resolution. In this work, we proposed a probabilistic LOR (pLOR) position technique that addresses axial and transaxial LOR grouping in 32 bit data. Second, two simplified approaches for 3D time-of-flight (TOF) scatter estimation were developed to accelerate the computationally intensive calculation without compromising accuracy. The proposed list-mode reconstruction algorithm was compared to the manufacturer's point spread function + TOF (PSF+TOF) algorithm. Phantom, animal, and human studies demonstrated that MOLAR with pLOR gives slightly faster contrast recovery than the PSF+TOF algorithm that uses the average 32 bit LOR sinogram positioning. Moving phantom and a whole-body human study suggested that event-by-event motion correction reduces image blurring caused by respiratory motion. We conclude that list-mode reconstruction with pLOR positioning provides a platform to generate high quality images for the mCT, and to recover fine structures in whole-body PET scans through event-by-event motion correction.

The effect of regularization in motion compensated PET image reconstruction: a realistic numerical 4D simulation study

Following continuous improvement in PET spatial resolution, respiratory motion correction has become an important task. Two of the most common approaches that utilize all detected PET events to motion-correct PET data are the reconstruct-transform-average method (RTA) and motion-compensated image reconstruction (MCIR). In RTA, separate images are reconstructed for each respiratory frame, subsequently transformed to one reference frame and finally averaged to produce a motion-corrected image. In MCIR, the projection data from all frames are reconstructed by including motion information in the system matrix so that a motion-corrected image is reconstructed directly. Previous theoretical analyses have explained why MCIR is expected to outperform RTA. It has been suggested that MCIR creates less noise than RTA because the images for each separate respiratory frame will be severely affected by noise. However, recent investigations have shown that in the unregularized case RTA images can have fewer noise artefacts, while MCIR images are more quantitatively accurate but have the common salt-and-pepper noise. In this paper, we perform a realistic numerical 4D simulation study to compare the advantages gained by including regularization within reconstruction for RTA and MCIR, in particular using the median-root-prior incorporated in the ordered subsets maximum a posteriori one-step-late algorithm. In this investigation we have demonstrated that MCIR with proper regularization parameters reconstructs lesions with less bias and root mean square error and similar CNR and standard deviation to regularized RTA. This finding is reproducible for a variety of noise levels (25, 50, 100 million counts), lesion sizes (8 mm, 14 mm diameter) and iterations. Nevertheless, regularized RTA can also be a practical solution for motion compensation as a proper level of regularization reduces both bias and mean square error.

Analysis and comparison of two methods for motion correction in PET imaging

PURPOSE

Although there have been various proposed methods for positron emission tomography (PET) motion correction, there is not sufficient evidence to answer which method is better in practice. This investigation aims to characterize the behavior of the two main motion-correction approaches in terms of convergence and image properties.

METHODS

For the first method, reconstruct-transform-average (RTA), reconstructions of each gate are transformed to a reference gate and averaged. In the second method, motion-compensated image reconstruction (MCIR), motion information is incorporated within the reconstruction. Both techniques studied were based on the ordered subsets expectation maximization algorithm. Motion information was obtained from a dynamic MR acquisition performed on a human volunteer and concurrent PET data were simulated from the dynamic MR data. The two approaches were assessed statistically using multiple realizations to accurately define the noise properties of the reconstructed images.

RESULTS

MCIR successfully recovers the true values of all regions, whereas RTA has high bias due to the limited count-statistics and interpolation errors during the transformation step. In addition, RTA noise is very small and stabilized, whereas in MCIR noise becomes progressively greater with the number of iterations and therefore MCIR outperforms RTA in terms of MSE only if noise is treated. For example, MCIR with postfiltering results in MSE up to 42% lower than RTA.

CONCLUSIONS

This study indicates that MCIR may provide superior performance overall to RTA if noise is minimized. However, in applications where quantification is not the main objective RTA can be a practical and simple method to correct for motion.