Spatial resolution properties of motion-compensated tomographic image reconstruction methods

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.

Motion estimation and correction in SPECT, PET and CT

Patient motion impacts single photon emission computed tomography (SPECT), positron emission tomography (PET) and X-ray computed tomography (CT) by giving rise to projection data inconsistencies that can manifest as reconstruction artifacts, thereby degrading image quality and compromising accurate image interpretation and quantification. Methods to estimate and correct for patient motion in SPECT, PET and CT have attracted considerable research effort over several decades. The aims of this effort have been two-fold: to estimate relevant motion fields characterizing the various forms of voluntary and involuntary motion; and to apply these motion fields within a modified reconstruction framework to obtain motion-corrected images. The aims of this review are to outline the motion problem in medical imaging and to critically review published methods for estimating and correcting for the relevant motion fields in clinical and preclinical SPECT, PET and CT. Despite many similarities in how motion is handled between these modalities, utility and applications vary based on differences in temporal and spatial resolution. Technical feasibility has been demonstrated in each modality for both rigid and non-rigid motion, but clinical feasibility remains an important target. There is considerable scope for further developments in motion estimation and correction, and particularly in data-driven methods that will aid clinical utility. State-of-the-art machine learning methods may have a unique role to play in this context.

Impact of motion compensation and partial volume correction for 18F-NaF PET/CT imaging of coronary plaque

Recent studies have suggested that ¹⁸F-NaF-PET enables visualization and quantification of plaque micro-calcification in the coronary tree. However, PET imaging of plaque calcification in the coronary arteries is challenging because of the respiratory and cardiac motion as well as partial volume effects. The objective of this work is to implement an image reconstruction framework, which incorporates compensation for respiratory as well as cardiac motion (MoCo) and partial volume correction (PVC), for cardiac ¹⁸F-NaF PET imaging in PET/CT. We evaluated the effect of MoCo and PVC on the quantification of vulnerable plaques in the coronary arteries. Realistic simulations (Biograph TPTV, Biograph mCT) and phantom acquisitions (Biograph mCT) were used for these evaluations. Different uptake values in the calcified plaques were evaluated in the simulations, while three 'plaque-type' lesions of 36, 31 and 18 mm³ were included in the phantom experiments. After validation, the MoCo and PVC methods were applied in four pilot NaF-PET patient studies. In all cases, the MoCo-based image reconstruction was performed using the STIR software. The PVC was obtained from a local projection (LP) method, previously evaluated in preclinical and clinical PET. The results obtained show a significant increase of the measured lesion-to-background ratios (LBR) in the MoCo  +  PVC images. These ratios were further enhanced when using directly the tissue-activities from the LP method, making this approach more suitable for the quantitative evaluation of coronary plaques. When using the LP method on the MoCo images, LBR increased between 200% and 1119% in the simulated data, between 212% and 614% in the phantom experiments and between 46% and 373% in the plaques with positive uptake observed in the pilot patients. In conclusion, we have built and validated a STIR framework incorporating MoCo and PVC for ¹⁸F-NaF PET imaging of coronary plaques. First results indicate an improved quantification of plaque-type lesions.

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.

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.

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.

Self-gated radial MRI for respiratory motion compensation on hybrid PET/MR systems

Accurate localization and uptake quantification of lesions in the chest and abdomen using PET imaging is challenging due to the respiratory motion during the exam. The advent of hybrid PET/MR systems offers new ways to compensate for respiratory motion without exposing the patient to additional radiation. The use of self-gated reconstructions of a 3D radial stack-of-stars GRE acquisition is proposed to derive a high-resolution MRI motion model. The self-gating signal is used to perform respiratory binning of the simultaneously acquired PET raw data. Matching mu-maps are generated for every bin, and post-reconstruction registration is performed in order to obtain a motion-compensated PET volume from the individual gates. The proposed method is demonstrated in-vivo for three clinical patients. Motion-corrected reconstructions are compared against ungated and gated PET reconstructions. In all cases, motion-induced blurring of lesions in the liver and lung was substantially reduced, without compromising SNR as it is the case for gated reconstructions.

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).

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

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.

Noise properties of motion-compensated tomographic image reconstruction methods

Motion-compensated image reconstruction (MCIR) methods incorporate motion models to improve image quality in the presence of motion. MCIR methods differ in terms of how they use motion information and they have been well studied separately. However, there have been less theoretical comparisions of different MCIR methods. This paper compares the theoretical noise properties of three popular MCIR methods assuming known nonrigid motion. We show the relationship among three MCIR methods-motion-compensated temporal regularization (MTR), the parametric motion model (PMM), and post-reconstruction motion correction (PMC)-for penalized weighted least square cases. These analyses show that PMM and MTR are matrix-weighted sums of all registered image frames, while PMC is a scalar-weighted sum. We further investigate the noise properties of MCIR methods with Poisson models and quadratic regularizers by deriving accurate and fast variance prediction formulas using an "analytical approach." These theoretical noise analyses show that the variances of PMM and MTR are lower than or comparable to the variance of PMC due to the statistical weighting. These analyses also facilitate comparisons of the noise properties of different MCIR methods, including the effects of different quadratic regularizers, the influence of the motion through its Jacobian determinant, and the effect of assuming that total activity is preserved. Two-dimensional positron emission tomography simulations demonstrate the theoretical results.

Modeling and Simulation of 4D PET-CT and PET-MR Images

The driving force in the research and development of new hybrid PET-CT/MR imaging scanners is the production of images with optimum quality, accuracy, and resolution. However, the acquisition process is limited by several factors. Key issues are the respiratory and cardiac motion artifacts that occur during an imaging session. In this article the necessary tools for modeling and simulation of realistic high-resolution four-dimensional PET-CT and PET-MR imaging data are described. Beyond the need for four-dimensional simulations, accurate modeling of the acquisition process can be included within the reconstruction algorithms assisting in the improvement of image quality and accuracy of estimation of physiologic parameters from four-dimensional hybrid PET imaging.