An EM algorithm for estimating SPECT emission and transmission parameters from emissions data only

The SNR of time-of-flight positron emission tomography data for joint reconstruction of the activity and attenuation images

Objective.Measurement of the time-of-flight (TOF) difference of each coincident pair of photons increases the effective sensitivity of positron emission tomography (PET). Many authors have analyzed the benefit of TOF for quantification and hot spot detection in the reconstructed activity images. However, TOF not only improves the effective sensitivity, it also enables the joint reconstruction of the tracer concentration and attenuation images. This can be used to correct for errors in CT- or MR-derived attenuation maps, or to apply attenuation correction without the help of a second modality. This paper presents an analysis of the effect of TOF on the variance of the jointly reconstructed attenuation and (attenuation corrected) tracer concentration images.Approach.The analysis is performed for PET systems that have a distribution of possibly non-Gaussian TOF-kernels, and includes the conventional Gaussian TOF-kernel as a special case. Non-Gaussian TOF-kernels are often observed in novel detector designs, which make use of two (or more) different mechanisms to convert the incoming 511 keV photon to optical photons. The analytical result is validated with a simple 2D simulation.Main results.We show that if two different TOF-kernels are equivalent for image reconstruction with known attenuation, then they are also equivalent for joint reconstruction of the activity and the attenuation images. The variance increase in the activity, caused by also jointly reconstructing the attenuation image, vanishes when the TOF-resolution approaches perfection.Significance.These results are of interest for PET detector development and for the development of stand-alone PET systems.

Deep-learning-based methods of attenuation correction for SPECT and PET

Attenuation correction (AC) is essential for quantitative analysis and clinical diagnosis of single-photon emission computed tomography (SPECT) and positron emission tomography (PET). In clinical practice, computed tomography (CT) is utilized to generate attenuation maps (μ-maps) for AC of hybrid SPECT/CT and PET/CT scanners. However, CT-based AC methods frequently produce artifacts due to CT artifacts and misregistration of SPECT-CT and PET-CT scans. Segmentation-based AC methods using magnetic resonance imaging (MRI) for PET/MRI scanners are inaccurate and complicated since MRI does not contain direct information of photon attenuation. Computational AC methods for SPECT and PET estimate attenuation coefficients directly from raw emission data, but suffer from low accuracy, cross-talk artifacts, high computational complexity, and high noise level. The recently evolving deep-learning-based methods have shown promising results in AC of SPECT and PET, which can be generally divided into two categories: indirect and direct strategies. Indirect AC strategies apply neural networks to transform emission, transmission, or MR images into synthetic μ-maps or CT images which are then incorporated into AC reconstruction. Direct AC strategies skip the intermediate steps of generating μ-maps or CT images and predict AC SPECT or PET images from non-attenuation-correction (NAC) SPECT or PET images directly. These deep-learning-based AC methods show comparable and even superior performance to non-deep-learning methods. In this article, we first discussed the principles and limitations of non-deep-learning AC methods, and then reviewed the status and prospects of deep-learning-based methods for AC of SPECT and PET.

Attenuation Correction for Dedicated Cardiac SPECT Imaging Without Using Transmission Data

Objectives

Attenuation correction (AC) using transmission scanning-like computed tomography (CT) is the standard method to increase the accuracy of cardiac single-photon emission computed tomography (SPECT) images. Recently developed dedicated cardiac SPECT do not support CT, and thus, scans on these systems are vulnerable to attenuation artifacts. This study presented a new method for generating an attenuation map directly from emission data by segmentation of precisely non-rigid registration extended cardiac-torso (XCAT)-digital phantom with cardiac SPECT images.

Methods

In-house developed non-rigid registration algorithm automatically aligns the XCAT- phantom with cardiac SPECT image to precisely segment the contour of organs. Pre-defined attenuation coefficients for given photon energies were assigned to generate attenuation maps. The CT-based attenuation maps were used for validation with which cardiac SPECT/CT data of 38 patients were included. Segmental myocardial counts of a 17-segment model from these databases were compared based on the basis of the paired t-test.

Results

The mean, and standard deviation of the mean square error and structural similarity index measure of the female stress phase between the proposed attenuation maps and the CT attenuation maps were 6.99±1.23% and 92±2.0%, of the male stress were 6.87±3.8% and 96±1.0%. Proposed attenuation correction and computed tomography based attenuation correction average myocardial perfusion count was significantly higher than that in non-AC in the mid-inferior, mid-lateral, basal-inferior, and lateral regions (p<0.001).

Conclusion

The proposed attenuation maps showed good agreement with the CT-based attenuation map. Therefore, it is feasible to enable AC for a dedicated cardiac SPECT or SPECT standalone scanners.

Convolutional neural network based attenuation correction for123I-FP-CIT SPECT with focused striatum imaging

SPECT imaging with¹²³I-FP-CIT is used for diagnosis of neurodegenerative disorders like Parkinson's disease. Attenuation correction (AC) can be useful for quantitative analysis of¹²³I-FP-CIT SPECT. Ideally, AC would be performed based on attenuation maps (μ-maps) derived from perfectly registered CT scans. Suchμ-maps, however, are most times not available and possible errors in image registration can induce quantitative inaccuracies in AC corrected SPECT images. Earlier, we showed that a convolutional neural network (CNN) based approach allows to estimate SPECT-alignedμ-maps for full brain perfusion imaging using only emission data. Here we investigate the feasibility of similar CNN methods for axially focused¹²³I-FP-CIT scans. We tested our approach on a high-resolution multi-pinhole prototype clinical SPECT system in a Monte Carlo simulation study. Three CNNs that estimateμ-maps in a voxel-wise, patch-wise and image-wise manner were investigated. As the added value of AC on clinical¹²³I-FP-CIT scans is still debatable, the impact of AC was also reported to check in which cases CNN based AC could be beneficial. AC using the ground truthμ-maps (GT-AC) and CNN estimatedμ-maps (CNN-AC) were compared with the case when no AC was done (No-AC). Results show that the effect of using GT-AC versus CNN-AC or No-AC on striatal shape and symmetry is minimal. Specific binding ratios (SBRs) from localized regions show a deviation from GT-AC≤2.5% for all three CNN-ACs while No-AC systematically underestimates SBRs by 13.1%. A strong correlation (r≥0.99) was obtained between GT-AC based SBRs and SBRs from CNN-ACs and No-AC. Absolute quantification (in kBq ml^-1) shows a deviation from GT-AC within 2.2% for all three CNN-ACs and of 71.7% for No-AC. To conclude, all three CNNs show comparable performance in accurateμ-map estimation and¹²³I-FP-CIT quantification. CNN-estimatedμ-map can be a promising substitute for CT-basedμ-map.

A physics and learning-based transmission-less attenuation compensation method for SPECT

Attenuation compensation (AC) is a pre-requisite for reliable quantification and beneficial for visual interpretation tasks in single-photon emission computed tomography (SPECT). Typical AC methods require the availability of an attenuation map, which is obtained using a transmission scan, such as a CT scan. This has several disadvantages such as increased radiation dose, higher costs, and possible misalignment between SPECT and CT scans. Also, often a CT scan is unavailable. In this context, we and others are showing that scattered photons in SPECT contain information to estimate the attenuation distribution. To exploit this observation, we propose a physics and learning-based method that uses the SPECT emission data in the photopeak and scatter windows to perform transmission-less AC in SPECT. The proposed method uses data acquired in the scatter window to reconstruct an initial estimate of the attenuation map using a physics-based approach. A convolutional neural network is then trained to segment this initial estimate into different regions. Pre-defined attenuation coefficients are assigned to these regions, yielding the reconstructed attenuation map, which is then used to reconstruct the activity distribution using an ordered subsets expectation maximization (OSEM)-based reconstruction approach. We objectively evaluated the performance of this method using highly realistic simulation studies conducted on the clinically relevant task of detecting perfusion defects in myocardial perfusion SPECT. Our results showed no statistically significant differences between the performance achieved using the proposed method and that with the true attenuation maps. Visually, the images reconstructed using the proposed method looked similar to those with the true attenuation map. Overall, these results provide evidence of the capability of the proposed method to perform transmission-less AC and motivate further evaluation.

Fisher information analysis of list-mode SPECT emission data for joint estimation of activity and attenuation distribution

The potential to perform attenuation and scatter compensation (ASC) in single-photon emission computed tomography (SPECT) imaging without a separate transmission scan is highly significant. In this context, attenuation in SPECT is primarily due to Compton scattering, where the probability of Compton scatter is proportional to the attenuation coefficient of the tissue and the energy of the scattered photon and the scattering angle are related. Based on this premise, we investigated whether the SPECT scattered-photon data acquired in list-mode (LM) format and including the energy information can be used to estimate the attenuation map. For this purpose, we propose a Fisher-information-based method that yields the Cramer-Rao bound (CRB) for the task of jointly estimating the activity and attenuation distribution using only the SPECT emission data. In the process, a path-based formalism to process the LM SPECT emission data, including the scattered-photon data, is proposed. The Fisher information method was implemented on NVIDIA graphics processing units (GPU) for acceleration. The method was applied to analyze the information content of SPECT LM emission data, which contains up to first-order scattered events, in a simulated SPECT system with parameters modeling a clinical system using realistic computational studies with 2-D digital synthetic and anthropomorphic phantoms. The method was also applied to LM data containing up to second-order scatter for a synthetic phantom. Experiments with anthropomorphic phantoms simulated myocardial perfusion and dopamine transporter (DaT)-Scan SPECT studies. The results show that the CRB obtained for the attenuation and activity coefficients was typically much lower than the true value of these coefficients. An increase in the number of detected photons yielded lower CRB for both the attenuation and activity coefficients. Further, we observed that systems with better energy resolution yielded a lower CRB for the attenuation coefficient. Overall, the results provide evidence that LM SPECT emission data, including the scattered photons, contains information to jointly estimate the activity and attenuation coefficients.

Deep learning-based attenuation map generation for myocardial perfusion SPECT

PURPOSE

Attenuation correction using CT transmission scanning increases the accuracy of single-photon emission computed tomography (SPECT) and enables quantitative analysis. Current existing SPECT-only systems normally do not support transmission scanning and therefore scans on these systems are susceptible to attenuation artifacts. Moreover, the use of CT scans also increases radiation dose to patients and significant artifacts can occur due to the misregistration between the SPECT and CT scans as a result of patient motion. The purpose of this study is to develop an approach to estimate attenuation maps directly from SPECT emission data using deep learning methods.

METHODS

Both photopeak window and scatter window SPECT images were used as inputs to better utilize the underlying attenuation information embedded in the emission data. The CT-based attenuation maps were used as labels with which cardiac SPECT/CT images of 65 patients were included for training and testing. We implemented and evaluated deep fully convolutional neural networks using both standard training and training using an adversarial strategy.

RESULTS

The synthetic attenuation maps were qualitatively and quantitatively consistent with the CT-based attenuation map. The globally normalized mean absolute error (NMAE) between the synthetic and CT-based attenuation maps were 3.60% ± 0.85% among the 25 testing subjects. The SPECT reconstructed images corrected using the CT-based attenuation map and synthetic attenuation map are highly consistent. The NMAE between the reconstructed SPECT images that were corrected using the synthetic and CT-based attenuation maps was 0.26% ± 0.15%, whereas the localized absolute percentage error was 1.33% ± 3.80% in the left ventricle (LV) myocardium and 1.07% ± 2.58% in the LV blood pool.

CONCLUSION

We developed a deep convolutional neural network to estimate attenuation maps for SPECT directly from the emission data. The proposed method is capable of generating highly reliable attenuation maps to facilitate attenuation correction for SPECT-only scanners for myocardial perfusion imaging.

Simultaneous Emission-Transmission Tomography in an MRI Hardware Framework

Multi-modality imaging is essential for diagnosis and therapy in challenging cases. A Holy Grail of medical imaging is a hybrid imaging system combining computed tomography (CT), nuclear imaging, and magnetic resonance imaging (MRI) to deliver registered morphological, functional, and cellular/molecular information simultaneously and quantitatively for precision medicine. Recently, a unique imaging approach was demonstrated that combines nuclear imaging with polarized radiotracers and MRI-based spatial encoding. The detection scheme exploits the directional preference of γ-rays emitted from the polarized nuclei, and the result is a concentration image with resolution that can outperform standard nuclear imaging at a sensitivity significantly higher than that of MRI. However, the method does not calculate the attenuation image. Here we propose to obtain MRI-modulated γ-ray data for simultaneous image reconstruction of emission and transmission parameters, which could serve as a stepping stone toward simultaneous CT-SPECT-MRI. This method acquires synchronized datasets to provide insight into morphological features and molecular activities with accurate spatiotemporal registration. We present a complete overview of the system design and the formulation for tomographic reconstruction when the distribution of polarized radiotracers is either global or limited to a region of interest (ROI). Numerical results support the feasibility of our approach and suggest further research topics.

Joint estimation of activity image and attenuation sinogram using time-of-flight positron emission tomography data consistency condition filtering

Attenuation correction is essential for quantitative reliability of positron emission tomography (PET) imaging. In time-of-flight (TOF) PET, attenuation sinogram can be determined up to a global constant from noiseless emission data due to the TOF PET data consistency condition. This provides the theoretical basis for jointly estimating both activity image and attenuation sinogram/image directly from TOF PET emission data. Multiple joint estimation methods, such as maximum likelihood activity and attenuation (MLAA) and maximum likelihood attenuation correction factor (MLACF), have already been shown that can produce improved reconstruction results in TOF cases. However, due to the nonconcavity of the joint log-likelihood function and Poisson noise presented in PET data, the iterative method still requires proper initialization and well-designed regularization to prevent convergence to local maxima. To address this issue, we propose a joint estimation of activity image and attenuation sinogram using the TOF PET data consistency condition as an attenuation sinogram filter, and then evaluate the performance of the proposed method using computer simulations.

An Expectation Maximization Method for Joint Estimation of Emission Activity Distribution and Photon Attenuation Map in PET

A maximum likelihood expectation maximization (MLEM) method is proposed for joint estimation of emission activity distribution and photon attenuation map from positron emission tomography (PET) emission data alone. The method is appealing since: (i) it guarantees monotonic likelihood increase to a local extremum, (ii) does not require arbitrary parameters, and (iii) guarantees the positivity of the estimated distributions. Moreover, we propose a discrete Poisson data acquisition model and numerical algorithm for: (i) efficient graphics processing unit (GPU) based formulation, and (ii) a closed form exact solution for the MLEM update equations, which is essential for accurate and robust estimation. Numerical experiments indicate that in the presence of noise, joint EMAA estimation converges to the true emission activity distribution with root mean square errors of 4% and 0.5% respectively in estimation of lung- and myocardial emission activity distributions for a computational XCAT thorax phantom.

Optimized MLAA for quantitative non-TOF PET/MR of the brain

For quantitative tracer distribution in positron emission tomography, attenuation correction is essential. In a hybrid PET/CT system the CT images serve as a basis for generation of the attenuation map, but in PET/MR, the MR images do not have a similarly simple relationship with the attenuation map. Hence attenuation correction in PET/MR systems is more challenging. Typically either of two MR sequences are used: the Dixon or the ultra-short time echo (UTE) techniques. However these sequences have some well-known limitations. In this study, a reconstruction technique based on a modified and optimized non-TOF MLAA is proposed for PET/MR brain imaging. The idea is to tune the parameters of the MLTR applying some information from an attenuation image computed from the UTE sequences and a T1w MR image. In this MLTR algorithm, an [Formula: see text] parameter is introduced and optimized in order to drive the algorithm to a final attenuation map most consistent with the emission data. Because the non-TOF MLAA is used, a technique to reduce the cross-talk effect is proposed. In this study, the proposed algorithm is compared to the common reconstruction methods such as OSEM using a CT attenuation map, considered as the reference, and OSEM using the Dixon and UTE attenuation maps. To show the robustness and the reproducibility of the proposed algorithm, a set of 204 [¹⁸F]FDG patients, 35 [¹¹C]PiB patients and 1 [¹⁸F]FET patient are used. The results show that by choosing an optimized value of [Formula: see text] in MLTR, the proposed algorithm improves the results compared to the standard MR-based attenuation correction methods (i.e. OSEM using the Dixon or the UTE attenuation maps), and the cross-talk and the scale problem are limited.

Attenuation correction in emission tomography using the emission data--A review

The problem of attenuation correction (AC) for quantitative positron emission tomography (PET) had been considered solved to a large extent after the commercial availability of devices combining PET with computed tomography (CT) in 2001; single photon emission computed tomography (SPECT) has seen a similar development. However, stimulated in particular by technical advances toward clinical systems combining PET and magnetic resonance imaging (MRI), research interest in alternative approaches for PET AC has grown substantially in the last years. In this comprehensive literature review, the authors first present theoretical results with relevance to simultaneous reconstruction of attenuation and activity. The authors then look back at the early history of this research area especially in PET; since this history is closely interwoven with that of similar approaches in SPECT, these will also be covered. We then review algorithmic advances in PET, including analytic and iterative algorithms. The analytic approaches are either based on the Helgason-Ludwig data consistency conditions of the Radon transform, or generalizations of John's partial differential equation; with respect to iterative methods, we discuss maximum likelihood reconstruction of attenuation and activity (MLAA), the maximum likelihood attenuation correction factors (MLACF) algorithm, and their offspring. The description of methods is followed by a structured account of applications for simultaneous reconstruction techniques: this discussion covers organ-specific applications, applications specific to PET/MRI, applications using supplemental transmission information, and motion-aware applications. After briefly summarizing SPECT applications, we consider recent developments using emission data other than unscattered photons. In summary, developments using time-of-flight (TOF) PET emission data for AC have shown promising advances and open a wide range of applications. These techniques may both remedy deficiencies of purely MRI-based AC approaches in PET/MRI and improve standalone PET imaging.

A Novel Iterative CT Reconstruction Approach Based on FBP Algorithm

The Filtered Back-Projection (FBP) algorithm and its modified versions are the most important techniques for CT (Computerized tomography) reconstruction, however, it may produce aliasing degradation in the reconstructed images due to projection discretization. The general iterative reconstruction (IR) algorithms suffer from their heavy calculation burden and other drawbacks. In this paper, an iterative FBP approach is proposed to reduce the aliasing degradation. In the approach, the image reconstructed by FBP algorithm is treated as the intermediate image and projected along the original projection directions to produce the reprojection data. The difference between the original and reprojection data is filtered by a special digital filter, and then is reconstructed by FBP to produce a correction term. The correction term is added to the intermediate image to update it. This procedure can be performed iteratively to improve the reconstruction performance gradually until certain stopping criterion is satisfied. Some simulations and tests on real data show the proposed approach is better than FBP algorithm or some IR algorithms in term of some general image criteria. The calculation burden is several times that of FBP, which is much less than that of general IR algorithms and acceptable in the most situations. Therefore, the proposed algorithm has the potential applications in practical CT systems.

Joint Estimation of Activity and Attenuation in Whole-Body TOF PET/MRI Using Constrained Gaussian Mixture Models

It has recently been shown that the attenuation map can be estimated from time-of-flight (TOF) PET emission data using joint maximum likelihood reconstruction of attenuation and activity (MLAA). In this work, we propose a novel MRI-guided MLAA algorithm for emission-based attenuation correction in whole-body PET/MR imaging. The algorithm imposes MR spatial and CT statistical constraints on the MLAA estimation of attenuation maps using a constrained Gaussian mixture model (GMM) and a Markov random field smoothness prior. Dixon water and fat MR images were segmented into outside air, lung, fat and soft-tissue classes and an MR low-intensity (unknown) class corresponding to air cavities, cortical bone and susceptibility artifacts. The attenuation coefficients over the unknown class were estimated using a mixture of four Gaussians, and those over the known tissue classes using unimodal Gaussians, parameterized over a patient population. To eliminate misclassification of spongy bones with surrounding tissues, and thus include them in the unknown class, we heuristically suppressed fat in water images and also used a co-registered bone probability map. The proposed MLAA-GMM algorithm was compared with the MLAA algorithms proposed by Rezaei and Salomon using simulation and clinical studies with two different tracer distributions. The results showed that our proposed algorithm outperforms its counterparts in suppressing the cross-talk and scaling problems of activity and attenuation and thus produces PET images of improved quantitative accuracy. It can be concluded that the proposed algorithm effectively exploits the MR information and can pave the way toward accurate emission-based attenuation correction in TOF PET/MRI.

Emission-based estimation of lung attenuation coefficients for attenuation correction in time-of-flight PET/MR

In standard segmentation-based MRI-guided attenuation correction (MRAC) of PET data on hybrid PET/MRI systems, the inter/intra-patient variability of linear attenuation coefficients (LACs) is ignored owing to the assignment of a constant LAC to each tissue class. This can lead to PET quantification errors, especially in the lung regions. In this work, we aim to derive continuous and patient-specific lung LACs from time-of-flight (TOF) PET emission data using the maximum likelihood reconstruction of activity and attenuation (MLAA) algorithm. The MLAA algorithm was constrained for estimation of lung LACs only in the standard 4-class MR attenuation map using Gaussian lung tissue preference and Markov random field smoothness priors. MRAC maps were derived from segmentation of CT images of 19 TOF-PET/CT clinical studies into background air, lung, soft tissue and fat tissue classes, followed by assignment of predefined LACs of 0, 0.0224, 0.0864 and 0.0975 cm(-1), respectively. The lung LACs of the resulting attenuation maps were then estimated from emission data using the proposed MLAA algorithm. PET quantification accuracy of MRAC and MLAA methods was evaluated against the reference CT-based AC method in the lungs, lesions located in/near the lungs and neighbouring tissues. The results show that the proposed MLAA algorithm is capable of retrieving lung density gradients and compensate fairly for respiratory-phase mismatch between PET and corresponding attenuation maps. It was found that the mean of the estimated lung LACs generally follow the trend of the reference CT-based attenuation correction (CTAC) method. Quantitative analysis revealed that the MRAC method resulted in average relative errors of -5.2 ± 7.1% and -6.1 ± 6.7% in the lungs and lesions, respectively. These were reduced by the MLAA algorithm to -0.8 ± 6.3% and -3.3 ± 4.7%, respectively. In conclusion, we demonstrated the potential and capability of emission-based methods in deriving patient-specific lung LACs to improve the accuracy of attenuation correction in TOF PET/MR imaging, thus paving the way for their adaptation in the clinic.

Nonlinear dual reconstruction of SPECT activity and attenuation images

In single photon emission computed tomography (SPECT), accurate attenuation maps are needed to perform essential attenuation compensation for high quality radioactivity estimation. Formulating the SPECT activity and attenuation reconstruction tasks as coupled signal estimation and system parameter identification problems, where the activity distribution and the attenuation parameter are treated as random variables with known prior statistics, we present a nonlinear dual reconstruction scheme based on the unscented Kalman filtering (UKF) principles. In this effort, the dynamic changes of the organ radioactivity distribution are described through state space evolution equations, while the photon-counting SPECT projection data are measured through the observation equations. Activity distribution is then estimated with sub-optimal fixed attenuation parameters, followed by attenuation map reconstruction given these activity estimates. Such coupled estimation processes are iteratively repeated as necessary until convergence. The results obtained from Monte Carlo simulated data, physical phantom, and real SPECT scans demonstrate the improved performance of the proposed method both from visual inspection of the images and a quantitative evaluation, compared to the widely used EM-ML algorithms. The dual estimation framework has the potential to be useful for estimating the attenuation map from emission data only and thus benefit the radioactivity reconstruction.

ML-reconstruction for TOF-PET with simultaneous estimation of the attenuation factors

In positron emission tomography (PET), attenuation correction is typically done based on information obtained from transmission tomography. Recent studies show that time-of-flight (TOF) PET emission data allow joint estimation of activity and attenuation images. Mathematical analysis revealed that the joint estimation problem is determined up to a scale factor. In this work, we propose a maximum likelihood reconstruction algorithm that jointly estimates the activity image together with the sinogram of the attenuation factors. The algorithm is evaluated with 2-D and 3-D simulations as well as clinical TOF-PET measurements of a patient scan and compared to reference reconstructions. The robustness of the algorithm to possible imperfect scanner calibration is demonstrated with reconstructions of the patient scan ignoring the varying detector sensitivities.

Use of measured scatter data for the attenuation correction of single photon emission tomography without transmission scanning

PURPOSE

Attenuation correction is essential for reliable interpretation of emission tomography, however, the use of transmission measurements to generate attenuation maps is limited by availability of equipment and potential mismatches between the transmission and emission measurements. The authors present a first step toward a method of estimating an attenuation map from measured scatter data without a transmission scan.

METHODS

A scatter model has been developed that accurately predicts the distribution of photons which have been scattered once. The scatter model has been used as the basis of a maximum likelihood gradient ascent method to estimate an attenuation map from measured scatter data. In order to estimate both the attenuation map and activity distribution, iterations of the derived scatter based algorithm have been alternated with the maximum likelihood expectation maximization algorithm in a joint estimation process. For each iteration of the attenuation map estimation, the activity distribution is fixed at the values estimated during the previous activity iteration, and in each iteration of the activity distribution estimation the attenuation map is fixed at the values estimated during the previous attenuation iteration. The use of photopeak data to enhance the estimation of the attenuation map compared to the use of scatter data alone has also been considered. The algorithm derived has been used to reconstruct data simulated for an idealized two-dimensional situation and using a physical phantom.

RESULTS

The reconstruction of idealized data demonstrated good reconstruction of both the activity distribution and attenuation map. The inclusion of information recorded in the photopeak energy window in the attenuation map estimation step demonstrated an improvement in the accuracy of the reconstruction, enabling an accurate attenuation map to be recovered. Validation of the results with physical phantom data demonstrated that different regions of attenuation could be distinguished in a real situation and produces results that represent a promising first step toward the use of scatter data to estimate the activity distribution and attenuation map from single photon emission tomography (SPECT) data without a transmission scan.

CONCLUSIONS

The technique presented shows promise as a method of attenuation correction for SPECT data without the need for a separate transmission scan. Further work is required to further improve the method and to compensate for the assumptions used in the scatter model.

Transmission-less attenuation correction in time-of-flight PET: analysis of a discrete iterative algorithm

The maximum likelihood attenuation correction factors (MLACF) algorithm has been developed to calculate the maximum-likelihood estimate of the activity image and the attenuation sinogram in time-of-flight (TOF) positron emission tomography, using only emission data without prior information on the attenuation. We consider the case of a Poisson model of the data, in the absence of scatter or random background. In this case the maximization with respect to the attenuation factors can be achieved in a closed form and the MLACF algorithm works by updating the activity. Despite promising numerical results, the convergence of this algorithm has not been analysed. In this paper we derive the algorithm and demonstrate that the MLACF algorithm monotonically increases the likelihood, is asymptotically regular, and that the limit points of the iteration are stationary points of the likelihood. Because the problem is not convex, however, the limit points might be saddle points or local maxima. To obtain some empirical insight into the latter question, we present data obtained by applying MLACF to 2D simulated TOF data, using a large number of iterations and different initializations.

Simultaneous reconstruction of emission activity and attenuation coefficient distribution from TOF data, acquired with external transmission source

The simultaneous PET data reconstruction of emission activity and attenuation coefficient distribution is presented, where the attenuation image is constrained by exploiting an external transmission source. Data are acquired in time-of-flight (TOF) mode, allowing in principle for separation of emission and transmission data. Nevertheless, here all data are reconstructed at once, eliminating the need to trace the position of the transmission source in sinogram space. Contamination of emission data by the transmission source and vice versa is naturally modeled. Attenuated emission activity data also provide additional information about object attenuation coefficient values. The algorithm alternates between attenuation and emission activity image updates. We also proposed a method of estimation of spatial scatter distribution from the transmission source by incorporating knowledge about the expected range of attenuation map values. The reconstruction of experimental data from the Siemens mCT scanner suggests that simultaneous reconstruction improves attenuation map image quality, as compared to when data are separated. In the presented example, the attenuation map image noise was reduced and non-uniformity artifacts that occurred due to scatter estimation were suppressed. On the other hand, the use of transmission data stabilizes attenuation coefficient distribution reconstruction from TOF emission data alone. The example of improving emission images by refining a CT-based patient attenuation map is presented, revealing potential benefits of simultaneous CT and PET data reconstruction.

Joint reconstruction of activity and attenuation map using LM SPECT emission data

Attenuation and scatter correction in single photon emission computed tomography (SPECT) imaging often requires a computed tomography (CT) scan to compute the attenuation map of the patient. This results in increased radiation dose for the patient, and also has other disadvantages such as increased costs and hardware complexity. Attenuation in SPECT is a direct consequence of Compton scattering, and therefore, if the scattered photon data can give information about the attenuation map, then the CT scan may not be required. In this paper, we investigate the possibility of joint reconstruction of the activity and attenuation map using list-mode (LM) SPECT emission data, including the scattered-photon data. We propose a path-based formalism to process scattered-photon data. Following this, we derive analytic expressions to compute the Cramér-Rao bound (CRB) of the activity and attenuation map estimates, using which, we can explore the fundamental limit of information-retrieval capacity from LM SPECT emission data. We then suggest a maximum-likelihood (ML) scheme that uses the LM emission data to jointly reconstruct the activity and attenuation map. We also propose an expectation-maximization (EM) algorithm to compute the ML solution.

Anomaly Detection and Artifact Recovery in PET Attenuation-Correction Images Using the Likelihood Function

In dual modality PET/CT, CT data are used to generate the attenuation correction applied in the reconstruction of the PET emission image. This requires converting the CT image into a 511-keV attenuation map. Algorithms for making this transformation require assumptions about the makeup of material within the patient. Anomalous material such as contrast agent administered to enhance the CT scan confounds conversion algorithms and has been observed to result in inaccuracies, i.e., inconsistencies with the true 511-keV attenuation present at the time of the PET emission scan. These attenuation artifacts carry through to the final attenuation-corrected PET emission image and can resemble diseased tissue. We propose an approach to correcting this problem that employs the attenuation information carried by the PET emission data. A likelihood-based algorithm for identifying and correcting of contrast is presented and tested. The algorithm exploits the fact that contrast artifacts manifest as too-high attenuation values in an otherwise high quality attenuation image. In a separate study, the performance of the loglikelihood as an objective-function component of a detection/correction algorithm, independent of any particular algorithm was mapped out for several imaging scenarios as a function of statistical noise. Both the full algorithm and the loglikelihood performed well in studies with simulated data. Additional studies including those with patient data are required to fully understand their capabilities.

Completion of a truncated attenuation image from the attenuated PET emission data

Positron emission tomographs (PETs) are currently almost exclusively designed as hybrid systems. The current standard is the PET/CT combination, while prototype PET/MRI systems are being studied by several research groups. One problem in these systems is that the transaxial field-of-view of the second system is smaller than that of the PET camera and does not provide complete attenuation data. Because this second system provides the image for PET attenuation and scatter correction, the smaller FOV causes truncation of the attenuation map, producing bias in the attenuation corrected activity image. In this paper, we propose a maximum-a-posteriori algorithm for estimating the missing part of the attenuation map from the PET emission data. The method is evaluated on five artificially truncated 18F-FDGPET/CT studies, where it reduced the error on the reconstructed PET activities from 20% to less than 7%. The results on a PET/MRI patient study with 18F-FDG are presented as well.

Simultaneous reconstruction of activity and attenuation in time-of-flight PET

In positron emission tomography (PET) and single photon emission tomography (SPECT), attenuation correction is necessary for quantitative reconstruction of the tracer distribution. Previously, several attempts have been made to estimate the attenuation coefficients from emission data only. These attempts had limited success, because the problem does not have a unique solution, and severe and persistent "cross-talk" between the estimated activity and attenuation distributions was observed. In this paper, we show that the availability of time-of-flight (TOF) information eliminates the cross-talk problem by destroying symmetries in the associated Fisher information matrix. We propose a maximum-a-posteriori reconstruction algorithm for jointly estimating the attenuation and activity distributions from TOF PET data. The performance of the algorithm is studied with 2-D simulations, and further illustrated with phantom experiments and with a patient scan. The estimated attenuation image is robust to noise, and does not suffer from the cross-talk that was observed in non-TOF PET. However, some constraining is still mandatory, because the TOF data determine the attenuation sinogram only up to a constant offset.

Time-of-flight PET data determine the attenuation sinogram up to a constant

In positron emission tomography (PET), a quantitative reconstruction of the tracer distribution requires accurate attenuation correction. We consider situations where a direct measurement of the attenuation coefficient of the tissues is not available or is unreliable, and where one attempts to estimate the attenuation sinogram directly from the emission data by exploiting the consistency conditions that must be satisfied by the non-attenuated data. We show that in time-of-flight PET, the attenuation sinogram is determined by the emission data except for a constant and that its gradient can be estimated efficiently using a simple analytic algorithm. The stability of the method is illustrated numerically by means of a 2D simulation.

Simultaneous reconstruction of activity and attenuation for PET/MR

Medical investigations targeting a quantitative analysis of the position emission tomography (PET) images require the incorporation of additional knowledge about the photon attenuation distribution in the patient. Today, energy range adapted attenuation maps derived from computer tomography (CT) scans are used to effectively compensate for image quality degrading effects, such as attenuation and scatter. Replacing CT by magnetic resonance (MR) is considered as the next evolutionary step in the field of hybrid imaging systems. However, unlike CT, MR does not measure the photon attenuation and thus does not provide an easy access to this valuable information. Hence, many research groups currently investigate different technologies for MR-based attenuation correction (MR-AC). Typically, these approaches are based on techniques such as special acquisition sequences (alone or in combination with subsequent image processing), anatomical atlas registration, or pattern recognition techniques using a data base of MR and corresponding CT images. We propose a generic iterative reconstruction approach to simultaneously estimate the local tracer concentration and the attenuation distribution using the segmented MR image as anatomical reference. Instead of applying predefined attenuation values to specific anatomical regions or tissue types, the gamma attenuation at 511 keV is determined from the PET emission data. In particular, our approach uses a maximum-likelihood estimation for the activity and a gradient-ascent based algorithm for the attenuation distribution. The adverse effects of scattered and accidental gamma coincidences on the quantitative accuracy of PET, as well as artifacts caused by the inherent crosstalk between activity and attenuation estimation are efficiently reduced using enhanced decay event localization provided by time-of-flight PET, accurate correction for accidental coincidences, and a reduced number of unknown attenuation coefficients. First results achieved with measured whole body PET data and reference segmentation from CT showed an absolute mean difference of 0.005 cm⁻¹ (< 20%) in the lungs, 0.0009 cm⁻¹ (< 2%) in case of fat, and 0.0015 cm⁻¹ (< 2%) for muscles and blood. The proposed method indicates a robust and reliable alternative to other MR-AC approaches targeting patient specific quantitative analysis in time-of-flight PET/MR.

Attenuation map estimation with SPECT emission data only

Quantitative SPECT can be well achieved if photon attenuation is taken into account in the reconstruction process. Using a transmission scan is a common approach. A dramatic simplification could be made if the attenuation map could be obtained from the emission data. In this paper, we propose a new method to estimate the attenuation map using the data consistency conditions of the attenuated Radon transform. It is based on deriving boundaries of the constant regions of the true attenuation map using an iterative algorithm. This new method is tested by Monte Carlo simulations with the attenuation and scattering effects.

Simultaneous reconstruction of tissue attenuation and radioactivity maps in SPECT

The importance of accurate attenuation correction in single photon emission computed tomography (SPECT) has been widely recognized. In this paper, we propose a novel scheme of simultaneous reconstruction of the tissue attenuation map and the radioactivity distribution from SPECT emission sinograms, which is obviously beneficial when the transmission data is missing for cost or efficiency reasons. Our strategy combines the SPECT image formation and data measurement models, whereas the attenuation parameters are treated as random variables with known prior statistics. After converting the models to state space representation, the extended Kalman filtering procedures are adopted to linearize the equations and to provide the joint estimates in an approximate optimal sense. Experiments have been performed on synthetic data and real scanning data to illustrate abilities and benefits of the method.

Strategies for attenuation compensation in neurological PET studies

Molecular brain imaging using positron emission tomography (PET) has evolved into a vigorous academic field and is progressively gaining importance in the clinical arena. Significant progress has been made in the design of high-resolution three-dimensional (3-D) PET units dedicated to brain research and the development of quantitative imaging protocols incorporating accurate image correction techniques and sophisticated image reconstruction algorithms. However, emerging clinical and research applications of molecular brain imaging demand even greater levels of accuracy and precision and therefore impose more constraints with respect to the quantitative capability of PET. It has long been recognized that photon attenuation in tissues is the most important physical factor degrading PET image quality and quantitative accuracy. Quantitative PET image reconstruction requires an accurate attenuation map of the object under study for the purpose of attenuation compensation. Several methods have been devised to correct for photon attenuation in neurological PET studies. Significant attention has been devoted to optimizing computational performance and to balancing conflicting requirements. Approximate methods suitable for clinical routine applications and more complicated approaches for research applications, where there is greater emphasis on accurate quantitative measurements, have been proposed. The number of scientific contributions related to this subject has been increasing steadily, which motivated the writing of this review as a snapshot of the dynamically changing field of attenuation correction in cerebral 3D PET. This paper presents the physical and methodological basis of photon attenuation and summarizes state of the art developments in algorithms used to derive the attenuation map aiming at accurate attenuation compensation of brain PET data. Future prospects, research trends and challenges are identified and directions for future research are discussed.

Quantitative image reconstruction in PET from emission data only using cluster analysis

Quantitative image reconstruction in positron emission tomography requires attenuation correction. In case the attenuation correction is not measured separately, under certain conditions this can be determined from the emission data alone. We present a method based on cluster analysis that assumes only 3 empirical attenuation coefficients, i.e., 0.095 cm-1 for soft tissue, 0.02 cm-1 for lung, and 0 cm-1 for air. The subsequent image reconstruction takes place in an iterative fashion, through maximization of image likelihood. For the mathematical thorax phantom used in the present study, the results are comparable to those obtained after separate measurement of the attenuation correction.

Simultaneous iterative reconstruction of emission and attenuation images in positron emission tomography from emission data only

For quantitative image reconstruction in positron emission tomography attenuation correction is mandatory. In case that no data are available for the calculation of the attenuation correction factors one can try to determine them from the emission data alone. However, it is not clear if the information content is sufficient to yield an adequate attenuation correction together with a satisfactory activity distribution. Therefore, we determined the log likelihood distribution for a thorax phantom depending on the choice of attenuation and activity pixel values to measure the crosstalk between both. In addition an iterative image reconstruction (one-dimensional Newton-type algorithm with a maximum likelihood estimator), which simultaneously reconstructs the images of the activity distribution and the attenuation coefficients is used to demonstrate the problems and possibilities of such a reconstruction. As result we show that for a change of the log likelihood in the range of statistical noise, the associated change in the activity value of a structure is between 6% and 263%. In addition, we show that it is not possible to choose the best maximum on the basis of the log likelihood when a regularization is used, because the coupling between different structures mediated by the (smoothing) regularization prevents an adequate solution due to crosstalk. We conclude that taking into account the attenuation information in the emission data improves the performance of image reconstruction with respect to the bias of the activities, however, the reconstruction still is not quantitative.

Modeling the axial extension of a transmission line source within iterative reconstruction via multiple transmission sources

Reconstruction algorithms for transmission tomography have generally assumed that the photons reaching a particular detector bin at a particular angle originate from a single point source. In this paper, we highlight several cases of extended transmission sources, in which it may be useful to approach the estimation of attenuation coefficients as a problem involving multiple transmission point sources. Examined in detail is the case of a fixed transmission line source with a fan-beam collimator. This geometry can result in attenuation images that have significant axial blur. Herein it is also shown, empirically, that extended transmission sources can result in biased estimates of the average attenuation, and an explanation is proposed. The finite axial resolution of the transmission line source configuration is modeled within iterative reconstruction using an expectation-maximization algorithm that was previously derived for estimating attenuation coefficients from single photon emission computed tomography (SPECT) emission data. The same algorithm is applicable to both problems because both can be thought of as involving multiple transmission sources. It is shown that modeling axial blur within reconstruction removes the bias in the average estimated attenuation and substantially improves the axial resolution of attenuation images.