Reconstruction of attenuation map using discrete consistency conditions

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.

A review of PET attenuation correction methods for PET-MR

Despite being thirteen years since the installation of the first PET-MR system, the scanners constitute a very small proportion of the total hybrid PET systems installed. This is in stark contrast to the rapid expansion of the PET-CT scanner, which quickly established its importance in patient diagnosis within a similar timeframe. One of the main hurdles is the development of an accurate, reproducible and easy-to-use method for attenuation correction. Quantitative discrepancies in PET images between the manufacturer-provided MR methods and the more established CT- or transmission-based attenuation correction methods have led the scientific community in a continuous effort to develop a robust and accurate alternative. These can be divided into four broad categories: (i) MR-based, (ii) emission-based, (iii) atlas-based and the (iv) machine learning-based attenuation correction, which is rapidly gaining momentum. The first is based on segmenting the MR images in various tissues and allocating a predefined attenuation coefficient for each tissue. Emission-based attenuation correction methods aim in utilising the PET emission data by simultaneously reconstructing the radioactivity distribution and the attenuation image. Atlas-based attenuation correction methods aim to predict a CT or transmission image given an MR image of a new patient, by using databases containing CT or transmission images from the general population. Finally, in machine learning methods, a model that could predict the required image given the acquired MR or non-attenuation-corrected PET image is developed by exploiting the underlying features of the images. Deep learning methods are the dominant approach in this category. Compared to the more traditional machine learning, which uses structured data for building a model, deep learning makes direct use of the acquired images to identify underlying features. This up-to-date review goes through the literature of attenuation correction approaches in PET-MR after categorising them. The various approaches in each category are described and discussed. After exploring each category separately, a general overview is given of the current status and potential future approaches along with a comparison of the four outlined categories.

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.

Feasibility of attenuation map alignment in pinhole cardiac SPECT using exponential data consistency conditions

PURPOSE

Dedicated cardiac SPECT systems do not typically include an integrated CT scanner and thus attenuation correction requires registration of separately acquired transmission scans. Data consistency conditions are equations that express the redundancy between projections while taking into account the attenuation effects. This study assessed the feasibility of applying exponential data consistency conditions to rebinned pinhole projections for attenuation-map registration in pinhole cardiac SPECT.

METHODS

Simulations of an anthropomorphic computer phantom with three different tracer activity distributions were performed with and without clinical levels of noise in the projection data. The first activity distribution contained activity only within the myocardium which satisfied the assumptions of the data consistency conditions. The other two distributions violated these assumptions by adding background activity and uptake in the liver. Simulations included acquisitions with 360, 31, and 9 pinhole projections and detector pixel sizes of 0.75 and 2.5 mm. A metric based on the average difference between pairs of exponential projections was used to evaluate registration accuracy.

RESULTS

When activity is restricted to the myocardium, the registration error was 3.0 mm for 31 noisy pinhole projections with a detector size of 2.5 mm. When activity is added to the background and the liver, a correction for the extra-cardiac activity is needed but when applied, a registration error of 6.0 mm was achieved.

CONCLUSION

These results suggest that it may be feasible to use exponential data consistency conditions to register pinhole cardiac SPECT and CT transmission data. Taxonomy: 8-6 (IM-SPECT/Registration).

PET/MRI attenuation estimation in the lung: A review of past, present, and potential techniques

Positron emission tomography/magnetic resonance imaging (PET/MRI) potentially offers several advantages over positron emission tomography/computed tomography (PET/CT), for example, no CT radiation dose and soft tissue images from MR acquired at the same time as the PET. However, obtaining accurate linear attenuation correction (LAC) factors for the lung remains difficult in PET/MRI. LACs depend on electron density and in the lung, these vary significantly both within an individual and from person to person. Current commercial practice is to use a single‐valued population‐based lung LAC, and better estimation is needed to improve quantification. Given the under‐appreciation of lung attenuation estimation as an issue, the inaccuracy of PET quantification due to the use of single‐valued lung LACs, the unique challenges of lung estimation, and the emerging status of PET/MRI scanners in lung disease, a review is timely. This paper highlights past and present methods, categorizing them into segmentation, atlas/mapping, and emission‐based schemes. Potential strategies for future developments are also presented.

Zero-Extra-Dose PET Delayed Imaging with Data-Driven Attenuation Correction Estimation

PURPOSE

Delayed positron emission tomography (PET) imaging may improve sensitivity and specificity in lesion detection. We proposed a PET data-driven method to estimate the attenuation map (AM) for the delayed scan without an additional x-ray computed tomography (CT).

PROCEDURES

An emission-attenuation-scatter joint estimation framework was developed. Several practical issues for clinical datasets were addressed. Particularly, the unknown scatter correction was incorporated in the joint estimation algorithm. The scaling problem was solved using prior information from the early CT scan. Fourteen patient datasets were added to evaluate the method. These patients went through two separate PET/CT scans. The delayed CT-based AM served as ground truth for the delayed scan. Standard uptake values (SUVmean and SUVmax) of lesion and normal tissue regions of interests (ROIs) in the early and delayed phase and the respective %DSUV (percentage change of SUVmean at two different time points) were analyzed, all with estimated and the true AM. Three radiologists participated in lesion detection tasks with images reconstructed with both AMs and rated scores for detectability.

RESULTS

The mean relative difference of SUVmean in lesion and normal liver tissue were 3.30 and 6.69 %. The average lesion-to-background contrast (detectability) with delayed PET images using CT AM was 60 % higher than that of the earlier PET image, and was 64 % higher when using the data-based AM. %DSUV for lesions and liver backgrounds with CT-based AM were - 0.058 ± 0.25 and - 0.33 ± 0.08 while with data-based AM were - 0.00 ± 0.26 and - 0.28 ± 0.08. Only slight significance difference was found between using CT-based AM and using the data-based AM reconstruction delay phase on %DSUV of lesion. The scores associated with the two AMs matched well consistently.

CONCLUSIONS

Our method may be used in delayed PET imaging, which allows no secondary CT radiation in delayed phase. The quantitative analysis for lesion detection purpose could be ensured.

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.

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.

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.

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.

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.

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.

Recent advances in iterative reconstruction for clinical SPECT/PET and CT

Statistical iterative reconstruction is now widely used in clinical practice and has contributed to significant improvement in image quality in recent years. Although primarily used for reconstruction in emission tomography (both single photon emission computed tomography (SPECT) and positron emission tomography (PET)) there is increasing interest in also applying similar algorithms to x-ray computed tomography (CT). There is increasing complexity in the factors that are included in the reconstruction, a demonstration of the versatility of the approach. Research continues with exploration of methods for further improving reconstruction quality with effective correction for various sources of artefact.

Attenuation correction in SPECT without attenuation map

A method of attenuation correction in Single Photon Emission Computed Tomography (SPECT), based on emission data only is presented. The algorithm uses the well known Helgason-Ludwig consistency conditions. However, it does not attempt to find the attenuation map, but rather the correction factors for the projection data, which makes the problem simpler and does not need to assume any particular template of the attenuation map. Although the method alone gives only approximate correction, it can be combined with other approaches to provide an effective improvement for scanning systems without the transmission scan functionality.

Fourier properties of the fan-beam sinogram

PURPOSE

P. R. Edholm, R. M. Lewitt, and B. Lindholm, "Novel properties of the Fourier decomposition of the sinogram," in Proceedings of the International Workshop on Physics and Engineering of Computerized Multidimensional Imaging and Processing [Proc. SPIE 671, 8-18 (1986)] described properties of a parallel beam projection sinogram with respect to its radial and angular frequencies. The purpose is to perform a similar derivation to arrive at corresponding properties of a fan-beam projection sinogram for both the equal-angle and equal-spaced detector sampling scenarios.

METHODS

One of the derived properties is an approximately zero-energy region in the two-dimensional Fourier transform of the full fan-beam sinogram. This region is in the form of a double-wedge, similar to the parallel beam case, but different in that it is asymmetric with respect to the frequency axes. The authors characterize this region for a point object and validate the derived properties in both a simulation and a head CT data set. The authors apply these results in an application using algebraic reconstruction.

RESULTS

In the equal-angle case, the domain of the zero region is (q,k) for which / k/(k-q) / > R/L, where q and k are the frequency variables associated with the detector and view angular positions, respectively, R is the radial support of the object, and L is the source-to-isocenter distance. A filter was designed to retain only sinogram frequencies corresponding to a specified radial support. The filtered sinogram was used to reconstruct the same radial support of the head CT data. As an example application of this concept, the double-wedge filter was used to computationally improve region of interest iterative reconstruction.

CONCLUSIONS

Interesting properties of the fan-beam sinogram exist and may be exploited in some applications.

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.

Advances in Attenuation Correction Techniques in PET

Molecular imaging using PET has evolved from a vigorous academic field into the clinical arena. Considerable advances have been made in the design of high-resolution standalone PET and combined PET/CT units dedicated to clinical whole-body scanning. Likewise, much worthwhile research focused on the development of quantitative imaging protocols incorporating accurate data correction techniques and sophisticated image reconstruction algorithms. Since its inception, photon attenuation in biological tissues has been identified as the most important physical degrading factor affecting PET image quality and quantitative accuracy. Various strategies have been devised to determine an accurate attenuation map to enable correction for nonlinear photon attenuation in whole-body PET studies. This article 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 PET data. Future prospects, research trends, and challenges are identified, and directions for future research are discussed.

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.

A new data consistency condition for fan-beam projection data

The sum of all attenuation data acquired in one view of parallel-beam projections is a view angle independent constant. This fact is known as a data consistency condition on the two-dimensional Radon transforms. It plays an important role in tomographic image reconstruction and artifact correction. In this paper, a novel fan-beam data consistency condition (FDCC) is derived and presented. Using the FDCC, individual projection data in one view of fan-beam projections can be estimated from filtering all other projection data measured from different view angles. Numerical simulations are performed to validate the new FDCC in correcting ring artifacts caused by malfunctioning detector cells.

Application of discrete data consistency conditions for selecting regularization parameters in PET attenuation map reconstruction

Simultaneous emission and transmission measurement is appealing in PET due to the matching of geometrical conditions between emission and transmission and reduced acquisition time for the study. A potential problem remains: when transmission statistics are low, attenuation correction could be very noisy. Although noise in the attenuation map can be controlled through regularization during statistical reconstruction, the selection of regularization parameters is usually empirical. In this paper, we investigate the use of discrete data consistency conditions (DDCC) to optimally select one or two regularization parameters. The advantages of the method are that the reconstructed attenuation map is consistent with the emission data and that it accounts for particularity in the emission reconstruction algorithm and acquisition geometry. The methodology is validated using a computer-generated whole-body phantom for both emission and transmission, neglecting random events and scattered radiation. MAP-TR was used for attenuation map reconstruction, while 3D OS-EM is used for estimating the emission image. The estimation of regularization parameters depends on the resolution of the emission image controlled by the number of iterations in OS-EM. The computer simulation shows that, on one hand, DDCC regularized attenuation map reduces propagation of the transmission scan noise to the emission image, while on the other hand DDCC prevents excessive attenuation map smoothing that could result in resolution mismatch artefacts between emission and transmission.

Magnetic resonance imaging-guided attenuation and scatter corrections in three-dimensional brain positron emission tomography

Reliable attenuation correction represents an essential component of the long chain of modules required for the reconstruction of artifact-free, quantitative brain positron emission tomography (PET) images. In this work we demonstrate the proof of principle of segmented magnetic resonance imaging (MRI)-guided attenuation and scatter corrections in three-dimensional (3D) brain PET. We have developed a method for attenuation correction based on registered T1-weighted MRI, eliminating the need of an additional transmission (TX) scan. The MR images were realigned to preliminary reconstructions of PET data using an automatic algorithm and then segmented by means of a fuzzy clustering technique which identifies tissues of significantly different density and composition. The voxels belonging to different regions were classified into air, skull, brain tissue and nasal sinuses. These voxels were then assigned theoretical tissue-dependent attenuation coefficients as reported in the ICRU 44 report followed by Gaussian smoothing and addition of a good statistics bed image. The MRI-derived attenuation map was then forward projected to generate attenuation correction factors (ACFs) to be used for correcting the emission (EM) data. The method was evaluated and validated on 10 patient data where TX and MRI brain images were available. Qualitative and quantitative assessment of differences between TX-guided and segmented MRI-guided 3D reconstructions were performed by visual assessment and by estimating parameters of clinical interest. The results indicated a small but noticeable improvement in image quality as a consequence of the reduction of noise propagation from TX into EM data. Considering the difficulties associated with preinjection TX-based attenuation correction and the limitations of current calculated attenuation correction, MRI-based attenuation correction in 3D brain PET would likely be the method of choice for the foreseeable future as a second best approach in a busy nuclear medicine center and could be applied to other functional brain imaging modalities such as SPECT.

Fuzzy clustering-based segmented attenuation correction in whole-body PET imaging

Segmented attenuation correction is now a widely accepted technique to reduce noise propagation from transmission scanning in positron emission tomography (PET). In this paper, we present a new method for segmenting transmission images in whole-body scanning. This reduces the noise in the correction maps while still correcting for differing attenuation coefficients of specific tissues. Based on the fuzzy C-means (FCM) algorithm, the method segments the PET transmission images into a given number of clusters to extract specific areas of differing attenuation such as air, the lungs and soft tissue, preceded by a median filtering procedure. The reconstructed transmission image voxels are, therefore, segmented into populations of uniform attenuation based on knowledge of the human anatomy. The clustering procedure starts with an overspecified number of clusters followed by a merging process to group clusters with similar properties (redundant clusters) and removal of some undesired substructures using anatomical knowledge. The method is unsupervised, adaptive and allows the classification of both pre- or post-injection transmission images obtained using either coincident 68Ge or single-photon 137Cs sources into main tissue components in terms of attenuation coefficients. A high-quality transmission image of the scanner bed is obtained from a high statistics scan and added to the transmission image. The segmented transmission images are then forward projected to generate attenuation correction factors to be used for the reconstruction of the corresponding emission scan. The technique has been tested on a chest phantom simulating the lungs, heart cavity and the spine, the Rando-Alderson phantom, and whole-body clinical PET studies showing a remarkable improvement in image quality, a clear reduction of noise propagation from transmission into emission data allowing for reduction of transmission scan duration. There was very good correlation (R2 = 0.96) between maximum standardized uptake values (SUVs) in lung nodules measured on images reconstructed with measured and segmented attenuation correction with a statistically significant decrease in SUV (17.03% +/- 8.4%, P < 0.01) on the latter images, whereas no proof of statistically significant differences on the average SUVs was observed. Finally, the potential of the FCM algorithm as a segmentation method and its limitations as well as other prospective applications of the technique are discussed.