Recovery of the spatially-variant deformations in dual-panel PET reconstructions using deep-learning.

Dual panel PET systems, such as Breast-PET (B-PET) scanner, exhibit strong asymmetric and anisotropic spatially-variant deformations in the reconstructed images due to the limited-angle data and strong depth of interaction effects for the oblique LORs inherent in such systems. In our previous work, we studied time-of-flight (TOF) effects and image-based spatially-variant PSF resolution models within dual-panel PET reconstruction to reduce these deformations. The application of PSF based models led to better and more uniform quantification of small lesions across the field of view (FOV). However, the ability of such a model to correct for PSF deformation is limited to small objects. On the other hand, large object deformations caused by the limited-angle reconstruction cannot be corrected with the PSF modeling alone. In this work, we investigate the ability of deep-learning (DL) networks to recover such strong spatially-variant image deformations using first simulated PSF deformations in image space of a generic dual panel PET system and then using simulated and acquired phantom reconstructions from dual panel B-PET system developed in our lab at University of Pennsylvania. For the studies using real B-PET data, the network was trained on the simulated synthetic data sets providing ground truth for objects resembling experimentally acquired phantoms on which the network deformation corrections were then tested. The synthetic and acquired limited-angle B-PET data were reconstructed using DIRECT-RAMLA reconstructions, which were then used as the network inputs. Our results demonstrate that DL approaches can significantly eliminate deformations of limited angle systems and improve their quantitative performance.

3D/4D Reconstruction and Quantitative Total Body Imaging.

Total-body PET image reconstruction follows a similar procedure to the image reconstruction process for standard whole-body PET scanners. One unique aspect of total-body imaging is simultaneous coverage of the entire human body, which makes it convenient to perform total-body dynamic PET scans. Therefore, four-dimensional dynamic PET reconstruction and parametric imaging are of great interest in total-body imaging. This article covers some basics of PET image reconstruction and then focuses on three- and four-dimensional PET reconstruction for total-body imaging. Methods for image formation from raw measurements in total-body PET are described. Challenges and opportunities in total-body PET image reconstruction are discussed.

Effects of TOF Resolution Models on Edge Artifacts in PET Reconstruction from Limited-Angle Data.

Limited-angle data, such as data obtained from a dual-panel Breast-PET scanner, result in substantial image blur in directions coinciding with the missing cone of the image spectrum. On systems with time-of-flight (TOF) capabilities, this blur is reduced as given by the TOF uncertainty, with the image spectrum being correspondingly expanded into the missing spectral cone. Modeling of the TOF uncertainty in the reconstruction is expected to deconvolve this residual TOF blurring. We have however observed that, as a tradeoff, this TOF de-blurring process also introduces ringing artifacts at the edges, analogous to the edge effects observed with line-of-response (LOR) resolution modeling, which attempts to deconvolve the blur due to detector resolution effects. However, in the former case, the ringing artifacts are much wider due to the spatial extent of the TOF uncertainty as compared to the width of typical LOR resolution blur. We illustrate and investigate the effects of using matched, as well as under-modeled and over-modeled, TOF kernels on edge artifacts in reconstruction from limited-angle data, and compare them with TOF reconstructions of complete data. Although for the conventional data with full angular coverage the reconstruction is fairly insensitive to the exact size of the TOF kernel and TOF modeling does not produce ringing artifacts, it is not the case for the limited-angle data. We show that it is important to use some form of regularization of the TOF uncertainty deconvolution process within reconstruction of the limited-angle data, such as decreasing the TOF kernel size.

Special Section Guest Editorial: Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine.

Guest editors Scott D. Metzler, Samuel Matej, and J. Webster Stayman provide an introduction to the Special Section on Three-Dimensional Image Reconstruction in Nuclear Medicine, PET, and CT.

Three-dimensional Fourier-based reprojection analytic reconstruction from histoprojections for high-resolution time-of-flight positron emission tomography scanners.

Purpose: In spite of the general acceptance of iterative reconstruction for clinical use, analytic algorithms provide an important alternative tool due to their linearity, unbiased performance, and predictability for quantitative imaging and quality control studies. On modern time-of-flight (TOF) positron emission tomography scanners with excellent timing resolution, substantial angular compression of (histoprojection) data is possible without loss of resolution, but this also brings challenges for analytical algorithms. We propose TOF and non-TOF Fourier-based analytic approaches that appropriately handle the data sparsity on modern TOF systems. Approach: The proposed TOF algorithm (3D-DIFTOF-direct inversion Fourier transform for TOF) works directly on histoprojection data. The proposed Fourier-based approaches for histoprojection data are further extended to include non-TOF reconstruction (TOF-binned 3D-DIFT), which is particularly useful in time calibration procedures due to its insensitivity to time calibration errors. TOF information is used here to extend available histoprojection data to a larger number of views, essential for artifact-free non-TOF reconstruction. The proposed algorithms are compared with standard analytic techniques on Siemens scanners-space-based confidence-weighted TOF FBP and non-TOF DIFT. Results: 3D-DIFTOF reconstruction demonstrates both improved NEMA-based resolution and contrast versus background variability trade-offs. Similarly, the TOF-binned 3D-DIFT approach shows improved contrast-noise trade-offs over the standard non-TOF approach and is well suited for timing calibration. Conclusions: Our results demonstrate that the proposed 3D-DIFTOF technique provides an improved and more faithful characterization of image resolution compared with standard space-based analytic reconstructions. The proposed tools also provide accurate translation of sparse TOF data available on clinical scanners to upsampled data for non-TOF algorithms.

Practical joint reconstruction of activity and attenuation with autonomous scaling for time-of-flight PET.

Recent research has showed that attenuation images can be determined from emission data, jointly with activity images, up to a scaling constant when utilizing the time-of-flight (TOF) information. We aim to develop practical CT-less joint reconstruction for clinical TOF PET scanners to obtain quantitatively accurate activity and attenuation images. In this work, we present a joint reconstruction of activity and attenuation based on MLAA (maximum likelihood reconstruction of attenuation and activity) with autonomous scaling determination and joint TOF scatter estimation from TOF PET data. Our idea for scaling is to use a selected volume of interest (VOI) in a reconstructed attenuation image with known attenuation, e.g. a liver in patient imaging. First, we construct a unit attenuation medium which has a similar, though not necessarily the same, support to the imaged emission object. All detectable LORs intersecting the unit medium have an attenuation factor of e -1≈ 0.3679, i.e. the line integral of linear attenuation coefficients is one. The scaling factor can then be determined from the difference between the reconstructed attenuation image and the known attenuation within the selected VOI normalized by the unit attenuation medium. A four-step iterative joint reconstruction algorithm is developed. In each iteration, (1) first the activity is updated using TOF OSEM from TOF list-mode data; (2) then the attenuation image is updated using XMLTR-a extended MLTR from non-TOF LOR sinograms; (3) a scaling factor is determined based on the selected VOI and both activity and attenuation images are updated using the estimated scaling; and (4) scatter is estimated using TOF single scatter simulation with the jointly reconstructed activity and attenuation images. The performance of joint reconstruction is studied using simulated data from a generic whole-body clinical TOF PET scanner and a long axial FOV research PET scanner as well as 3D experimental data from the PennPET Explorer scanner. We show that the proposed joint reconstruction with proper autonomous scaling provides low bias results comparable to the reference reconstruction with known attenuation.

Modelling and Simulation of Compton Scatter Image Formation in Positron Emission Tomography.

We present the comparative study of the analytical forward model and the statistical simulation of the Compton single scatter in the Positron Emission Tomography. The formula of the forward model has been obtained using the Single Scatter Simulation approximation under simplified assumptions and therefore we calculate scatter projections using independent Monte Carlo simulation mimicking the scatter physics. The numerical comparative study has been performed using a digital cylindrical phantom filled in with water and containing spherical sources of emission activity located at the central and several displaced positions. Good fits of the formula-based and statistically generated profiles of scatter projections are observed in the presented numerical results.

Spatially-variant image-based modeling of PSF deformations with application to a limited angle geometry from a dual-panel breast-PET imager.

Dual-panel PET system configuration can lead to spatially variable point-spread functions (PSF) of considerable deformations due to depth-of-interaction effects and limited angular coverage. If not modelled properly, these effects result in decreased and inconsistent recovery of lesion activity across the field-of-view (FOV), as well as mispositioning of lesions in the reconstructed image caused by strong PSF asymmetries. We implemented and evaluated models of such PSF deformations with spatially-variant image-based resolution modeling (IRM) within reconstruction (varRM) using the Direct Image REConstruction for Time-of-flight (DIRECT) method and within post-reconstruction deconvolution methods. In addition, DIRECT reconstruction was performed with a spatially-invariant IRM (invRM) and without resolution modeling (noRM) for comparison. The methods were evaluated using simulated data for a realistic breast model with a set of 5 mm lesions located throughout the FOV of a dual-panel Breast-PET scanner. We simulated high-count data to focus on the ability of each method to correctly recover the PSF deformations, and a clinically realistic count level to assess the impact of low count data on the quantitative performance of the evaluated techniques. Performance of the methods evaluated herein was assessed by comparing lesion activity recovery (%BIAS), consistency (%SD) across the FOV, overall error (%RMSE), and recovery of each lesion location. As expected, all techniques using IRM provide considerable improvement over the noRM reconstruction. For the high-count cases, the overall quantitative performance of all IRM techniques, whether within reconstruction or within post-reconstruction, is similar if the lesion location misplacements are ignored. However, invRM provides less consistent performance on activity across lesions and is not able to recover accurate lesion locations. For a clinically realistic count level, varRM reconstruction consistently outperforms all compared approaches, while the post-reconstruction IRM approaches exhibit higher %SD and %RMSE values due to being more affected by the data noise than the within-reconstruction IRM approaches.

Model-Based Normalization of a Fractional-Crystal Collimator for Small-Animal PET Imaging.

Previously, we proposed to use a coincidence collimator to achieve fractional-crystal resolution in PET imaging. We have designed and fabricated a collimator prototype for a small-animal PET scanner, A-PET. To compensate for imperfections in the fabricated collimator prototype, collimator normalization, as well as scanner normalization, is required to reconstruct quantitative and artifact-free images. In this study, we develop a normalization method for the collimator prototype based on the A-PET normalization using a uniform cylinder phantom. We performed data acquisition without the collimator for scanner normalization first, and then with the collimator from eight different rotation views for collimator normalization. After a reconstruction without correction, we extracted the cylinder parameters from which we generated expected emission sinograms. Single scatter simulation was used to generate the scattered sinograms. We used the least-squares method to generate the normalization coefficient for each LOR based on measured, expected and scattered sinograms. The scanner and collimator normalization coefficients were factorized by performing two normalizations separately. The normalization methods were also verified using experimental data acquired from A-PET with and without the collimator. In summary, we developed a model-base collimator normalization that can significantly reduce variance and produce collimator normalization with adequate statistical quality within feasible scan time.

Image-based Modeling of PSF Deformation with Application to Limited Angle PET Data.

The point-spread-functions (PSFs) of reconstructed images can be deformed due to detector effects such as resolution blurring and parallax error, data acquisition geometry such as insufficient sampling or limited angular coverage in dual-panel PET systems, or reconstruction imperfections/simplifications. PSF deformation decreases quantitative accuracy and its spatial variation lowers consistency of lesion uptake measurement across the imaging field-of-view (FOV). This can be a significant problem with dual panel PET systems even when using TOF data and image reconstruction models of the detector and data acquisition process. To correct for the spatially variant reconstructed PSF distortions we propose to use an image-based resolution model (IRM) that includes such image PSF deformation effects. Originally the IRM was mostly used for approximating data resolution effects of standard PET systems with full angular coverage in a computationally efficient way, but recently it was also used to mitigate effects of simplified geometric projectors. Our work goes beyond this by including into the IRM reconstruction imperfections caused by combination of the limited angle, parallax errors, and any other (residual) deformation effects and testing it for challenging dual panel data with strongly asymmetric and variable PSF deformations. We applied and tested these concepts using simulated data based on our design for a dedicated breast imaging geometry (B-PET) consisting of dual-panel, time-of-flight (TOF) detectors. We compared two image-based resolution models; i) a simple spatially invariant approximation to PSF deformation, which captures only the general PSF shape through an elongated 3D Gaussian function, and ii) a spatially variant model using a Gaussian mixture model (GMM) to more accurately capture the asymmetric PSF shape in images reconstructed from data acquired with the B-PET scanner geometry. Results demonstrate that while both IRMs decrease the overall uptake bias in the reconstructed image, the second one with the spatially variant and accurate PSF shape model is also able to ameliorate the spatially variant deformation effects to provide consistent uptake results independent of the lesion location within the FOV.

Analytic TOF PET reconstruction algorithm within DIRECT data partitioning framework.

Iterative reconstruction algorithms are routinely used for clinical practice; however, analytic algorithms are relevant candidates for quantitative research studies due to their linear behavior. While iterative algorithms also benefit from the inclusion of accurate data and noise models the widespread use of time-of-flight (TOF) scanners with less sensitivity to noise and data imperfections make analytic algorithms even more promising. In our previous work we have developed a novel iterative reconstruction approach (DIRECT: direct image reconstruction for TOF) providing convenient TOF data partitioning framework and leading to very efficient reconstructions. In this work we have expanded DIRECT to include an analytic TOF algorithm with confidence weighting incorporating models of both TOF and spatial resolution kernels. Feasibility studies using simulated and measured data demonstrate that analytic-DIRECT with appropriate resolution and regularization filters is able to provide matched bias versus variance performance to iterative TOF reconstruction with a matched resolution model.

A unified Fourier theory for time-of-flight PET data.

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D x-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions--the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are necessary and sufficient for 3D x-ray transform with TOF measurement. Finally, we give numerical examples of inverse rebinning for a 3D TOF PET and Fourier-based rebinning for a 2D TOF PET using the FORCEs to show the efficacy of the unified Fourier solutions.

Fourier rebinning and consistency equations for time-of-flight PET planograms.

Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give numerical examples of implementation of a fast 2D TOF planogram projector and Fourier-based rebinning for a 2D TOF planograms using the FORCEs to show the efficacy of the Fourier-based solutions.

Transmission-less attenuation estimation from time-of-flight PET histo-images using consistency equations.

In positron emission tomography (PET) imaging, attenuation correction with accurate attenuation estimation is crucial for quantitative patient studies. Recent research showed that the attenuation sinogram can be determined up to a scaling constant utilizing the time-of-flight information. The TOF-PET data can be naturally and efficiently stored in a histo-image without information loss, and the radioactive tracer distribution can be efficiently reconstructed using the DIRECT approaches. In this paper, we explore transmission-less attenuation estimation from TOF-PET histo-images. We first present the TOF-PET histo-image formation and the consistency equations in the histo-image parameterization, then we derive a least-squares solution for estimating the directional derivatives of the attenuation factors from the measured emission histo-images. Finally, we present a fast solver to estimate the attenuation factors from their directional derivatives using the discrete sine transform and fast Fourier transform while considering the boundary conditions. We find that the attenuation histo-images can be uniquely determined from the TOF-PET histo-images by considering boundary conditions. Since the estimate of the attenuation directional derivatives can be inaccurate for LORs tangent to the patient boundary, external sources, e.g. a ring or annulus source, might be needed to give an accurate estimate of the attenuation gradient for such LORs. The attenuation estimation from TOF-PET emission histo-images is demonstrated using simulated 2D TOF-PET data.

LOR-interleaving image reconstruction for PET imaging with fractional-crystal collimation.

Positron emission tomography (PET) has become an important modality in medical and molecular imaging. However, in most PET applications, the resolution is still mainly limited by the physical crystal sizes or the detector's intrinsic spatial resolution. To achieve images with better spatial resolution in a central region of interest (ROI), we have previously proposed using collimation in PET scanners. The collimator is designed to partially mask detector crystals to detect lines of response (LORs) within fractional crystals. A sequence of collimator-encoded LORs is measured with different collimation configurations. This novel collimated scanner geometry makes the reconstruction problem challenging, as both detector and collimator effects need to be modeled to reconstruct high-resolution images from collimated LORs. In this paper, we present a LOR-interleaving (LORI) algorithm, which incorporates these effects and has the advantage of reusing existing reconstruction software, to reconstruct high-resolution images for PET with fractional-crystal collimation. We also develop a 3D ray-tracing model incorporating both the collimator and crystal penetration for simulations and reconstructions of the collimated PET. By registering the collimator-encoded LORs with the collimator configurations, high-resolution LORs are restored based on the modeled transfer matrices using the non-negative least-squares method and EM algorithm. The resolution-enhanced images are then reconstructed from the high-resolution LORs using the MLEM or OSEM algorithm. For validation, we applied the LORI method to a small-animal PET scanner, A-PET, with a specially designed collimator. We demonstrate through simulated reconstructions with a hot-rod phantom and MOBY phantom that the LORI reconstructions can substantially improve spatial resolution and quantification compared to the uncollimated reconstructions. The LORI algorithm is crucial to improve overall image quality of collimated PET, which can have significant implications in preclinical and clinical ROI imaging applications.

Image reconstructions from super-sampled data sets with resolution modeling in PET imaging.

PURPOSE: Spatial resolution in positron emission tomography (PET) is still a limiting factor in many imaging applications. To improve the spatial resolution for an existing scanner with fixed crystal sizes, mechanical movements such as scanner wobbling and object shifting have been considered for PET systems. Multiple acquisitions from different positions can provide complementary information and increased spatial sampling. The objective of this paper is to explore an efficient and useful reconstruction framework to reconstruct super-resolution images from super-sampled low-resolution data sets. METHODS: The authors introduce a super-sampling data acquisition model based on the physical processes with tomographic, downsampling, and shifting matrices as its building blocks. Based on the model, we extend the MLEM and Landweber algorithms to reconstruct images from super-sampled data sets. The authors also derive a backprojection-filtration-like (BPF-like) method for the super-sampling reconstruction. Furthermore, they explore variant methods for super-sampling reconstructions: the separate super-sampling resolution-modeling reconstruction and the reconstruction without downsampling to further improve image quality at the cost of more computation. The authors use simulated reconstruction of a resolution phantom to evaluate the three types of algorithms with different super-samplings at different count levels. RESULTS: Contrast recovery coefficient (CRC) versus background variability, as an image-quality metric, is calculated at each iteration for all reconstructions. The authors observe that all three algorithms can significantly and consistently achieve increased CRCs at fixed background variability and reduce background artifacts with super-sampled data sets at the same count levels. For the same super-sampled data sets, the MLEM method achieves better image quality than the Landweber method, which in turn achieves better image quality than the BPF-like method. The authors also demonstrate that the reconstructions from super-sampled data sets using a fine system matrix yield improved image quality compared to the reconstructions using a coarse system matrix. Super-sampling reconstructions with different count levels showed that the more spatial-resolution improvement can be obtained with higher count at a larger iteration number. CONCLUSIONS: The authors developed a super-sampling reconstruction framework that can reconstruct super-resolution images using the super-sampling data sets simultaneously with known acquisition motion. The super-sampling PET acquisition using the proposed algorithms provides an effective and economic way to improve image quality for PET imaging, which has an important implication in preclinical and clinical region-of-interest PET imaging applications.

Resolution Enhancement in PET Reconstruction Using Collimation.

Collimation can improve both the spatial resolution and sampling properties compared to the same scanner without collimation. Spatial resolution improves because each original crystal can be conceptually split into two (i.e., doubling the number of in-plane crystals) by masking half the crystal with a high-density attenuator (e.g., tungsten); this reduces coincidence efficiency by 4× since both crystals comprising the line of response (LOR) are masked, but yields 4× as many resolution-enhanced (RE) LORs. All the new RE LORs can be measured by scanning with the collimator in different configurations. In this simulation study, the collimator was assumed to be ideal, neither allowing gamma penetration nor truncating the field of view. Comparisons were made in 2D between an uncollimated small-animal system with 2-mm crystals that were assumed to be perfectly absorbing and the same system with collimation that narrowed the effective crystal size to 1 mm. Digital phantoms included a hot-rod and a single-hot-spot, both in a uniform background with activity ratio of 4:1. In addition to the collimated and uncollimated configurations, angular and spatial wobbling acquisitions of the 2-mm case were also simulated. Similarly, configurations with different combinations of the RE LORs were considered including (i) all LORs, (ii) only those parallel to the 2-mm LORs; and (iii) only cross pairs that are not parallel to the 2-mm LORs. Lastly, quantitative studies were conducted for collimated and uncollimated data using contrast recovery coefficient and mean-squared error (MSE) as metrics. The reconstructions show that for most noise levels there is a substantial improvement in image quality (i.e., visual quality, resolution, and a reduction in artifacts) by using collimation even when there are 4× fewer counts or - in some cases - comparing with the noiseless uncollimated reconstruction. By comparing various configurations of sampling, the results show that it is the matched combination of both improved spatial resolution of each LOR and the increase in the number of LORs that yields improved reconstructions. Further, the quantitative studies show that for low-count scans, the collimated data give better MSE for small lesions and the uncollimated data give better MSE for larger lesions; for high-count studies, the collimated data yield better quantitative values for the entire range of lesion sizes that were evaluated.

Comparison of list-mode and DIRECT approaches for time-of-flight PET reconstruction.

Early clinical results with time-of-flight (TOF) positron emission tomography (PET) systems have demonstrated the advantages of TOF information in PET reconstruction. Reconstruction approaches in TOF-PET systems include list-mode and binned iterative algorithms as well as confidence-weighted analytic methods. List-mode iterative TOF reconstruction retains the resolutions of the data in the spatial and temporal domains without any binning approximations but is computationally intensive. We have developed an approach [DIRECT (direct image reconstruction for TOF)] to speed up TOF-PET reconstruction that takes advantage of the reduced angular sampling requirement of TOF data by grouping list-mode data into a small number of azimuthal views and co-polar tilts and depositing the grouped events into histo-images, arrays with the sampling and geometry of the final image. All physical effects are included in the system model and deposited in the same histo-image structure. Using histo-images allows efficient computation during reconstruction without ray-tracing or interpolation operations. The DIRECT approach was compared with 3-D list-mode TOF ordered subsets expectation maximization (OSEM) reconstruction for phantom and patient data taken on the University of Pennsylvania research LaBr (3) TOF-PET scanner. The total processing and reconstruction time for these studies with DIRECT without attention to code optimization is approximately 25%-30% that of list-mode TOF-OSEM to achieve comparable image quality. Furthermore, the reconstruction time for DIRECT is independent of the number of events and/or sizes of the spatial and TOF kernels, while the time for list-mode TOF-OSEM increases with more events or larger kernels. The DIRECT approach is able to reproduce the image quality of list-mode iterative TOF reconstruction both qualitatively and quantitatively in measured data with a reduced time.

Fisher information-based evaluation of image quality for time-of-flight PET.

The use of time-of-flight (TOF) information during positron emission tomography (PET) reconstruction has been found to improve the image quality. In this work we quantified this improvement using two existing methods: 1) a very simple analytical expression only valid for a central point in a large uniform disk source and 2) efficient analytical approximations for postfiltered maximum likelihood expectation maximization (MLEM) reconstruction with a fixed target resolution, predicting the image quality in a pixel or in a small region of interest based on the Fisher information matrix. Using this latter method the weighting function for filtered backprojection reconstruction of TOF PET data proposed by C. Watson can be derived. The image quality was investigated at different locations in various software phantoms. Simplified as well as realistic phantoms, measured both with TOF PET systems and with a conventional PET system, were simulated. Since the time resolution of the system is not always accurately known, the effect on the image quality of using an inaccurate kernel during reconstruction was also examined with the Fisher information-based method. First, we confirmed with this method that the variance improvement in the center of a large uniform disk source is proportional to the disk diameter and inversely proportional to the time resolution. Next, image quality improvement was observed in all pixels, but in eccentric and high-count regions the contrast-to-noise ratio (CNR) increased less than in central and low- or medium-count regions. Finally, the CNR was seen to decrease when the time resolution was inaccurately modeled (too narrow or too wide) during reconstruction. Although the maximum CNR is not very sensitive to the time resolution error, using an inaccurate TOF kernel tends to introduce artifacts in the reconstructed image.

Efficient 3-D TOF PET reconstruction using view-grouped histo-images: DIRECT-direct image reconstruction for TOF.

For modern time-of-flight (TOF) positron emission tomography (PET) systems, in which the number of possible lines of response and TOF bins is much larger than the number of acquired events, the most appropriate reconstruction approaches are considered to be list-mode methods. However, their shortcomings are relatively high computational costs for reconstruction and for sensitivity matrix calculation. Efficient treatment of TOF data within the proposed DIRECT approach is obtained by 1) angular (azimuthal and co-polar) grouping of TOF events to a set of views as given by the angular sampling requirements for the TOF resolution, and 2) deposition (weighted-histogramming) of these grouped events, and correction data, into a set of "histo-images," one histo-image per view. The histo-images have the same geometry (voxel grid, size and orientation) as the reconstructed image. The concept is similar to the approach involving binning of the TOF data into angularly subsampled histo-projections-projections expanded in the TOF directions. However, unlike binning into histo-projections, the deposition of TOF events directly into the image voxels eliminates the need for tracing and/or interpolation operations during the reconstruction. Together with the performance of reconstruction operations directly in image space, this leads to a very efficient implementation of TOF reconstruction algorithms. Furthermore, the resolution properties are not compromised either, since events are placed into the image elements of the desired size from the beginning. Concepts and efficiency of the proposed data partitioning scheme are demonstrated in this work by using the DIRECT approach in conjunction with the row-action maximum-likelihood (RAMLA) algorithm.