Simultaneous maximum a posteriori reconstruction of attenuation and activity distributions from emission sinograms

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.

Image artifacts from MR-based attenuation correction in clinical, whole-body PET/MRI

PURPOSE

Integrated whole-body PET/MRI tomographs have become available. PET/MR imaging has the potential to supplement, or even replace combined PET/CT imaging in selected clinical indications. However, this is true only if methodological pitfalls and image artifacts arising from novel MR-based attenuation correction (MR-AC) are fully understood.

RESULTS

Here we present PET/MR image artifacts following routine MR-AC, as most frequently observed in clinical operations of an integrated whole-body PET/MRI system.

CONCLUSION

A clinical adoption of integrated PET/MRI should entail the joint image display and interpretation of MR data, MR-based attenuation maps and uncorrected plus attenuation-corrected PET images in order to recognize potential pitfalls from MR-AC and to ensure clinically accurate image interpretation.

Simultaneous MR-compatible emission and transmission imaging for PET using time-of-flight information

Quantitative positron emission tomography (PET) imaging relies on accurate attenuation correction. Predicting attenuation values from magnetic resonance (MR) images is difficult because MR signals are related to proton density and relaxation properties of tissues. Here, we propose a method to derive the attenuation map from a transmission scan. An annulus transmission source is positioned inside the field-of-view of the PET scanner. First a blank scan is acquired. The patient is injected with FDG and placed inside the scanner. 511-keV photons coming from the patient and the transmission source are acquired simultaneously. Time-of-flight information is used to extract the coincident photons originating from the annulus. The blank and transmission data are compared in an iterative reconstruction method to derive the attenuation map. Simulations with a digital phantom were performed to validate the method. The reconstructed attenuation coefficients differ less than 5% in volumes of interest inside the lungs, bone, and soft tissue. When applying attenuation correction in the reconstruction of the emission data a standardized uptake value error smaller than 9% was obtained for all tissues. In conclusion, our method can reconstruct the attenuation map and the emission data from a simultaneous scan without prior knowledge about the anatomy or the attenuation coefficients of the tissues.

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.

MRI-based attenuation correction for whole-body PET/MRI: quantitative evaluation of segmentation- and atlas-based methods

PET/MRI is an emerging dual-modality imaging technology that requires new approaches to PET attenuation correction (AC). We assessed 2 algorithms for whole-body MRI-based AC (MRAC): a basic MR image segmentation algorithm and a method based on atlas registration and pattern recognition (AT&PR).

METHODS

Eleven patients each underwent a whole-body PET/CT study and a separate multibed whole-body MRI study. The MR image segmentation algorithm uses a combination of image thresholds, Dixon fat-water segmentation, and component analysis to detect the lungs. MR images are segmented into 5 tissue classes (not including bone), and each class is assigned a default linear attenuation value. The AT&PR algorithm uses a database of previously aligned pairs of MRI/CT image volumes. For each patient, these pairs are registered to the patient MRI volume, and machine-learning techniques are used to predict attenuation values on a continuous scale. MRAC methods are compared via the quantitative analysis of AC PET images using volumes of interest in normal organs and on lesions. We assume the PET/CT values after CT-based AC to be the reference standard.

RESULTS

In regions of normal physiologic uptake, the average error of the mean standardized uptake value was 14.1% ± 10.2% and 7.7% ± 8.4% for the segmentation and the AT&PR methods, respectively. Lesion-based errors were 7.5% ± 7.9% for the segmentation method and 5.7% ± 4.7% for the AT&PR method.

CONCLUSION

The MRAC method using AT&PR provided better overall PET quantification accuracy than the basic MR image segmentation approach. This better quantification was due to the significantly reduced volume of errors made regarding volumes of interest within or near bones and the slightly reduced volume of errors made regarding areas outside the lungs.

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.

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.

Why is TOF PET reconstruction a more robust method in the presence of inconsistent data?

In order to obtain an accurate and quantitative positron emission tomography (PET) image, emission data need to be corrected for random coincidences, photon attenuation and Compton scattering of photons in the tissue, and detector efficiency response or normalization. The accuracy of these corrections strongly affects the quality of the PET image. There is evidence that time-of-flight (TOF) PET reconstruction is less sensitive than non-TOF reconstruction to inconsistencies between emission data and corrections. The purpose of this study is to analyze and discuss such experimental evidence. In this work, inconsistent correction data (inconsistent normalization, absence of scatter correction and mismatched attenuation correction) are introduced in experimental phantom data. Both TOF and non-TOF reconstructed images are analyzed to examine the effect of flawed data. The behavior of TOF reconstruction in respiratory artifacts, a very common example of inconsistency in the data, is studied in patient images. TOF reconstruction is less sensitive to mismatched attenuation correction, erroneous normalization and poorly estimated scatter correction. Such robustness depends strongly on the time resolution of the TOF PET scanner. In particular, the robustness of TOF in the presence of attenuation correction inconsistencies is discussed, using a simulation of a simple model of respiratory artifacts. We expect new generations of PET scanners, with improved time resolution, to be less and less sensitive to poor quality normalization, scatter and attenuation corrections. This not only reduces artifacts in the PET image, but also opens the way to less stringent requirements for the quality of the CT image (reducing either the equipment cost or the dose to the patient), and for the normalization protocols (simplifying or shortening the normalization procedures). Moreover, TOF reconstruction can be beneficial in multimodalities such as PET/MR, where a direct attenuation measurement is not available and attenuation correction can only be approximated.

Feasibility of template-guided attenuation correction in cat brain PET imaging

PURPOSE

Attenuation correction (AC) is important in quantitative positron emission tomography (PET) imaging of medium-sized animals such as the cat. However, additional time for transmission (TX) scanning and tracer uptake is required in PET studies with animal-dedicated PET scanners because post-injection TX scanning is not available in these systems. The aim of this study was to validate a template-guided AC (TGAC) method that does not require TX PET data for AC in cat 2-deoxy-2-[F-(18)fluoro-D-glucose (FDG) brain PET imaging.

METHODS

PET scans were acquired using a microPET Focus 120 scanner. TX data were obtained using a (68)Ge point source before the injection of FDG. To generate the attention map (mu-map) template for the TGAC, a target image of emission (EM) PET was selected, and spatial normalization parameters of individual EM data onto the target were reapplied to the corresponding mu-maps. The inverse transformations of the mu-map template into the individual spaces were performed, and the transformed template was forward projected to generate the AC factor. The TGAC method was compared with measured AC (MAC) and calculated AC (CAC) methods using region of interest (ROI) and SPM analyses.

RESULTS

The ROI analysis showed that the activity of the TGAC EM PET images strongly correlated with those of the MAC data (y = 0.98x + 0.01, R(2) = 0.96). In addition, no significant difference was observed in the SPM analysis. By contrast, the CAC showed a significantly higher uptake in the deep gray regions compared to the MAC (corrected P < 0.05). The ROI correlation with MAC was worse than with the TGAC (R(2) = 0.84). In SPM analysis for the voxel-wise group comparisons between before and after the induction of deafness, only the TGAC showed equivalent results with the MAC.

CONCLUSIONS

The TGAC was reliable in cat FDG brain PET studies in terms of compatibility with the MAC method. The TGAC might be a useful option for increasing study throughput and decreasing the probability of subject movement. In addition, it might reduce the possible biological effects of long-term anesthesia on the cat brain in investigations using animal-dedicated PET scanners.

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.

Performance evaluation of an Inveon PET preclinical scanner

We evaluated the performance of an Inveon preclinical PET scanner (Siemens Medical Solutions), the latest MicroPET system. Spatial resolution was measured with a glass capillary tube (0.26 mm inside diameter, 0.29 mm wall thickness) filled with (18)F solution. Transaxial and axial resolutions were measured with the source placed parallel and perpendicular to the axis of the scanner. The sensitivity of the scanner was measured with a (22)Na point source, placed on the animal bed and positioned at different offsets from the center of the field of view (FOV), as well as at different energy and coincidence windows. The noise equivalent count rates (NECR) and the system scatter fraction were measured using rat-like (Phi = 60, L = 150 mm) and mouse-like (Phi = 25 mm, L = 70 mm) cylindrical phantoms. Line sources filled with high activity (18)F (>250 MBq) were inserted parallel to the axes of the phantoms (13.5 and 10 mm offset). For each phantom, list-mode data were collected over 24 h at 350-650 keV and 250-750 keV energy windows and 3.4 ns coincidence window. System scatter fraction was measured when the random event rates were below 1%. Performance phantoms consisting of cylinders with hot rod inserts filled with (18)F were imaged. In addition, we performed imaging studies that show the suitability of the Inveon scanner for imaging small structures such as those in mice with a variety of tracers. The radial, tangential and axial resolutions at the center of FOV were 1.46 mm, 1.49 and 1.15 mm, respectively. At a radial offset of 2 cm, the FWHM values were 1.73, 2.20 and 1.47 mm, respectively. At a coincidence window of 3.4 ns, the sensitivity was 5.75% for EW = 350-650 keV and 7.4% for EW = 250-750 keV. For an energy window of 350-650 keV, the peak NECR was 538 kcps at 131.4 MBq for the rat-like phantom, and 1734 kcps at 147.4 MBq for the mouse-like phantom. The system scatter fraction values were 0.22 for the rat phantom and 0.06 for the mouse phantom. The Inveon system presents high image resolution, low scatter fraction values and improved sensitivity and count rate performance.

Suppression of metal artifacts in CT using a reconstruction procedure that combines MAP and projection completion

Metal implants such as hip prostheses and dental fillings produce streak and star artifacts in the reconstructed computed tomography (CT) images. Due to these artifacts, the CT image may not be diagnostically usable. A new reconstruction procedure is proposed that reduces the streak artifacts and that might improve the diagnostic value of the CT images. The procedure starts with a maximum a posteriori (MAP) reconstruction using an iterative reconstruction algorithm and a multimodal prior. This produces an artifact-free constrained image. This constrained image is the basis for an image-based projection completion procedure. The algorithm was validated on simulations, phantom and patient data, and compared with other metal artifact reduction algorithms.

Impact of metal artefacts due to EEG electrodes in brain PET/CT imaging

The goal of this study is to investigate the impact of electroencephalogram (EEG) electrodes on the visual quality and quantification of (18)F-FDG PET images in neurological PET/CT examinations. For this purpose, the scans of 20 epilepsy patients with EEG monitoring were used. The CT data were reconstructed with filtered backprojection (FBP) and with a metal artefact reduction (MAR) algorithm. Both data sets were used for CT-based attenuation correction (AC) of the PET data. Also, a calculated AC (CALC) technique was considered. A volume of interest (VOI)-based analysis and a voxel-based quantitative analysis were performed to compare the different AC methods. Images were also evaluated visually by two observers. It was shown with simulations and phantom measurements that from the considered AC methods, the MAR-AC can be used as the reference in this setting. The visual assessment of PET images showed local hot spots outside the brain corresponding to the locations of the electrodes when using FBP-AC. In the brain, no abnormalities were observed. The quantitative analysis showed a very good correlation between PET-FBP-AC and PET-MAR-AC, with a statistically significant positive bias in the PET-FBP-AC images of about 5-7% in most brain voxels. There was also good correlation between PET-CALC-AC and PET-MAR-AC, but in the PET-CALC-AC images, regions with both a significant positive and negative bias were observed. EEG electrodes give rise to local hot spots outside the brain and a positive quantification bias in the brain. However, when diagnosis is made by mere visual assessment, the presence of EEG electrodes does not seem to alter the diagnosis. When quantification is performed, the bias becomes an issue especially when comparing brain images with and without EEG monitoring.

An outlook on x-ray CT research and development

Over the past decade, computed tomography (CT) theory, techniques and applications have undergone a rapid development. Since CT is so practical and useful, undoubtedly CT technology will continue advancing biomedical and non-biomedical applications. In this outlook article, we share our opinions on the research and development in this field, emphasizing 12 topics we expect to be critical in the next decade: analytic reconstruction, iterative reconstruction, local/interior reconstruction, flat-panel based CT, dual-source CT, multi-source CT, novel scanning modes, energy-sensitive CT, nano-CT, artifact reduction, modality fusion, and phase-contrast CT. We also sketch several representative biomedical applications.

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.

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.

Joint estimation of dynamic PET images and temporal basis functions using fully 4D ML-EM

A fully 4D joint-estimation approach to reconstruction of temporal sequences of 3D positron emission tomography (PET) images is proposed. The method estimates both a set of temporal basis functions and the corresponding coefficient for each basis function at each spatial location within the image. The joint estimation is performed through a fully 4D version of the maximum likelihood expectation maximization (ML-EM) algorithm in conjunction with two different models of the mean of the Poisson measured data. The first model regards the coefficients of the temporal basis functions as the unknown parameters to be estimated and the second model regards the temporal basis functions themselves as the unknown parameters. The fully 4D methodology is compared to the conventional frame-by-frame independent reconstruction approach (3D ML-EM) for varying levels of both spatial and temporal post-reconstruction smoothing. It is found that using a set of temporally extensive basis functions (estimated from the data by 4D ML-EM) significantly reduces the spatial noise when compared to the independent method for a given level of image resolution. In addition to spatial image quality advantages, for smaller regions of interest (where statistical quality is often limited) the reconstructed time-activity curves show a lower level of bias and a lower level of noise compared to the independent reconstruction approach. Finally, the method is demonstrated on clinical 4D PET data.

The influence of attenuation correction and reconstruction techniques on the detection of hypo-perfused lesions in brain SPECT images

BACKGROUND

We evaluated the effects of attenuation correction and reconstruction techniques on the detection of hypoperfused lesions in brain SPECT imaging.

METHODS

A software phantom was constructed using the data available on the BrainWeb database by assigning activity values to grey and white matter. The true attenuation map was generated by assigning attenuation coefficients to six different tissue classes to create a non-uniform attenuation map. The uniform attenuation map was calculated using an attenuation coefficient of 0.15 cm(-1). Hypoperfused lesions of varying intensities and sizes were added. The phantom was then projected as typical SPECT projection data, taking into account attenuation and collimator blurring with the addition of Poisson noise. The projection data were reconstructed using four different methods: filtered back-projection in combination with Chang's first-order attenuation correction using the uniform or the true attenuation map and maximum likelihood iterative reconstruction using the uniform or the true attenuation map. Different Gaussian post-smoothing kernels were applied onto the reconstructed images and the performance of each procedure was analysed using figures of merit such as signal-to-noise ratio, bias and variance.

RESULTS

Uniform attenuation correction offered only slight deterioration of the signal-to-noise ratio compared to the true attenuation map. Maximum likelihood produced superior signal-to-noise ratios and lower bias at the same variance in comparison to the filtered back-projection.

CONCLUSION

Uniform attenuation correction is adequate for lesion detection while maximum likelihood provides enhanced lesion detection when compared to filtered back-projection.

Monotonic penalized-likelihood image reconstruction for X-ray fluorescence computed tomography

In this paper, we derive a monotonic penalized-likelihood algorithm for image reconstruction in X-ray fluorescence computed tomography (XFCT) when the attenuation maps at the energies of the fluorescence X-rays are unknown. In XFCT, a sample is irradiated with pencil beams of monochromatic synchrotron radiation that stimulate the emission of fluorescence X-rays from atoms of elements whose K- or L-edges lie below the energy of the stimulating beam. Scanning and rotating the object through the beam allows for acquisition of a tomographic dataset that can be used to reconstruct images of the distribution of the elements in question. XFCT is a stimulated emission tomography modality, and it is thus necessary to correct for attenuation of the incident and fluorescence photons. The attenuation map is, however, generally known only at the stimulating beam energy and not at the energies of the various fluorescence X-rays of interest. We have developed a penalized-likelihood image reconstruction strategy for this problem. The approach alternates between updating the distribution of a given element and updating the attenuation map for that element's fluorescence X-rays. The approach is guaranteed to increase the penalized likelihood at each iteration. Because the joint objective function is not necessarily concave, the approach may drive the solution to a local maximum. To encourage the algorithm to seek out a reasonable local maximum, we include in the objective function a prior that encourages a relationship, based on physical considerations, between the fluorescence attenuation map and the distribution of the element being reconstructed.

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.

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.

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.

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.

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

A maximum-likelihood (ML) expectation-maximization (EM) algorithm (called EM-IntraSPECT) is presented for simultaneously estimating single photon emission computed tomography (SPECT) emission and attenuation parameters from emission data alone. The algorithm uses the activity within the patient as transmission tomography sources, with which attenuation coefficients can be estimated. For this initial study, EM-IntraSPECT was tested on computer-simulated attenuation and emission maps representing a simplified human thorax as well as on SPECT data obtained from a physical phantom. Two evaluations were performed. First, to corroborate the idea of reconstructing attenuation parameters from emission data, attenuation parameters (mu) were estimated with the emission intensities (lambda) fixed at their true values. Accurate reconstructions of attenuation parameters were obtained. Second, emission parameters lambda and attenuation parameters mu were simultaneously estimated from the emission data alone. In this case there was crosstalk between estimates of lambda and mu and final estimates of lambda and mu depended on initial values. Estimates degraded significantly as the support extended out farther from the body, and an explanation for this is proposed. In the EM-IntraSPECT reconstructed attenuation images, the lungs, spine, and soft tissue were readily distinguished and had approximately correct shapes and sizes. As compared with standard EM reconstruction assuming a fix uniform attenuation map, EM-IntraSPECT provided more uniform estimates of cardiac activity in the physical phantom study and in the simulation study with tight support, but less uniform estimates with a broad support. The new EM algorithm derived here has additional applications, including reconstructing emission and transmission projection data under a unified statistical model.

Image-correction techniques in SPECT

This overview takes a look at different correction techniques for Single Photon Emission Computed Tomography (SPECT). We discuss the influence of the detection system followed by the scatter and attenuation caused by the object of investigation. When possible we describe how the correction methods for the different physical effects can be incorporated in the reconstruction method, being either filtered backprojection or iterative reconstruction.

Simultaneous iterative reconstruction for emission and attenuation images in positron emission tomography

The quality of the attenuation correction strongly influences the outcome of the reconstructed emission scan in positron emission tomography. Usually the attenuation correction factors are calculated from the transmission and blank scan and thereafter applied during the reconstruction on the emission data. However, this is not an optimal treatment of the available data, because the emission data themselves contain additional information about attenuation: The optimal treatment must use this information for the determination of the attenuation correction factors. Therefore, our purpose is to investigate a simultaneous emission and attenuation image reconstruction using a maximum likelihood estimator, which takes the attenuation information in the emission data into account. The total maximum likelihood function for emission and transmission is used to derive a one-dimensional Newton-like algorithm for the calculation of the emission and attenuation image. Log-likelihood convergence, mean differences, and the mean of squared differences for the emission image and the attenuation correction factors of a mathematical thorax phantom were determined and compared. As a result we obtain images improved with respect to log likelihood in all cases and with respect to our figures of merit in most cases. We conclude that the simultaneous reconstruction can improve the performance of image reconstruction.

Reconstruction of attenuation map using discrete consistency conditions

Methods of quantitative emission computed tomography require compensation for linear photon attenuation. A current trend in single-photon emission computed tomography (SPECT) and positron emission tomography (PET) is to employ transmission scanning to reconstruct the attenuation map. Such an approach, however, considerably complicates both the scanner design and the data acquisition protocol. A dramatic simplification could be made if the attenuation map could be obtained directly from the emission projections, without the use of a transmission scan. This can be done by applying the consistency conditions that enable us to identify the operator of the problem and, thus, to reconstruct the attenuation map. In this paper, we propose a new approach based on the discrete consistency conditions. One of the main advantages of the suggested method over previously used continuous conditions is that it can easily be applied in various scanning configurations, including fully three-dimensional (3-D) data acquisition protocols. Also, it provides a stable numerical implementation, allowing us to avoid the crosstalk between the attenuation map and the source function. A computationally efficient algorithm is implemented by using the QR and Cholesky decompositions. Application of the algorithm to computer-generated and experimentally measured SPECT data is considered.

Three-dimensional attenuation map reconstruction using geometrical models and free-form deformations

We address the issue of using deformable models to reconstruct an unknown attenuation map of the torso from a set of transmission scans. We assume the three-dimensional (3-D) distribution of attenuation coefficients to be piecewise uniform. We represent the unknown distribution by a set of closed surfaces defining regions having the same attenuating properties. The methods of reconstruction published so far tend to directly deform the surfaces, the parameters being the surface elements. Rather than deforming the surfaces, we explore the possibility of deforming the space in which the geometrical primitives are contained. We focus on the use of free-form deformations (FFD's) to describe the continuous transformation of space used to match a set of transmission measurements. We illustrate this approach by reconstructing realistically simulated transmission scans of the torso with various noise levels and compare the results to standard reconstruction methods.

Calculation of attenuation factors from combined singles and coincidence emission projections

We have developed a simple method for determining coincidence attenuation-correction factors C (the inverse of the total attenuation factors) from collimated singles (SPECT) and coincidence [positron emission tomography (PET)] projections without transmission data. Attenuation-correction factor estimates are determined for individual lines of response (LOR's) independently. The required data can be acquired using a gamma-camera system with coincidence capabilities. A first-order approximation (R) of C for an LOR is given by the product of the singles count rates, taken at each end of the LOR divided by the square of the coincidence count rate. The method was tested using simulated singles and coincidence projections starting with emission and attenuation maps from patient PET scans. Noise and resolution effects were modeled in separate studies. In the noise-free, high-resolution simulations, a scatter plot of the C values versus the corresponding R values for all LOR's produces a well-defined trajectory with little variance. Values of lnR were reconstructed into good quality attenuation maps that compare favorably with the originals. We conclude that the method works well on ideal data. The introduction of noise results in degraded images. In a simulated patient study, lung and outer body boundaries were visible in images produced with 3.2 x 10(4) coincidence counts.