Single scan parameterization of space-variant point spread functions in image space via a printed array: the impact for two PET/CT scanners

Recent advances in combined Positron Emission Tomography and Magnetic Resonance Imaging

Hybrid imaging modalities combine two or more medical imaging techniques offering exciting new possibilities to image the structure, function and biochemistry of the human body in far greater detail than has previously been possible to improve patient diagnosis. In this context, simultaneous Positron Emission Tomography and Magnetic Resonance (PET/MR) imaging offers great complementary information, but it also poses challenges from the point of view of hardware and software compatibility. The PET signal may interfere with the MR magnetic field and vice-versa, posing several challenges and constrains in the PET instrumentation for PET/MR systems. Additionally, anatomical maps are needed to properly apply attenuation and scatter corrections to the resulting reconstructed PET images, as well motion estimates to minimize the effects of movement throughout the acquisition. In this review, we summarize the instrumentation implemented in modern PET scanners to overcome these limitations, describing the historical development of hybrid PET/MR scanners. We pay special attention to the methods used in PET to achieve attenuation, scatter and motion correction when it is combined with MR, and how both imaging modalities may be combined in PET image reconstruction algorithms.

Reconstruction of multi-animal PET acquisitions with anisotropically variant PSF

Among other factors such as random, attenuation and scatter corrections, uniform spatial resolution is key to performing accurate quantitative studies in Positron emission tomography (PET). Particularly in preclinical PET studies involving simultaneous acquisition of multiple animals, the degradation of image resolution due to the depth of interaction (DOI) effect far from the center of the Field of View (FOV) becomes a significant concern. In this work, we incorporated a spatially-variant resolution model into a real time iterative reconstruction code to obtain accurate images of multi-animal acquisition. We estimated the spatially variant point spread function (SV-PSF) across the FOV using measurements and Monte Carlo (MC) simulations. The SV-PSF obtained was implemented in a GPU-based Ordered subset expectation maximization (OSEM) reconstruction code, which includes scatter, attenuation and random corrections. The method was evaluated with acquisitions from two preclinical PET/CT scanners of the SEDECAL Argus family: a Derenzo phantom placed 2 cm off center in the 4R-SuperArgus, and a multi-animal study with 4 mice in the 6R-SuperArgus. The SV-PSF reconstructions showed uniform spatial resolution without significant increase in reconstruction time, with superior image quality compared to the uniform PSF model.

Photoacoustic Tomography Image Restoration With Measured Spatially Variant Point Spread Functions

The spatial resolution of photoacoustic tomography (PAT) can be characterized by the point spread function (PSF) of the imaging system. Due to the tomographic detection geometry, the PAT image degradation model could be generally described by using spatially variant PSFs. Deconvolution of the PAT image with these PSFs could restore image resolution and recover object details. Previous PAT image restoration algorithms assume that the degraded images can be restored by either a single uniform PSF, or some blind estimation of the spatially variant PSFs. In this work, we propose a PAT image restoration method to improve image quality and resolution based on experimentally measured spatially variant PSFs. Using photoacoustic absorbing microspheres, we design a rigorous PSF measurement procedure, and successfully acquire a dense set of spatially variant PSFs for a commercial cross-sectional PAT system. A pixel-wise PSF map is further obtained by employing a multi-Gaussian-based fitting and interpolation algorithm. To perform image restoration, an optimization-based iterative restoration model with two kinds of regularizations is proposed. We perform phantom and in vivo mice imaging experiments to verify the proposed method, and the results show significant image quality and resolution improvement.

Motion Dependent and Spatially Variant Resolution Modeling for PET Rigid Motion Correction

Recent advances in positron emission tomography (PET) have allowed to perform brain scans of freely moving animals by using rigid motion correction. One of the current challenges in these scans is that, due to the PET scanner spatially variant point spread function (SVPSF), motion corrected images have a motion dependent blurring since animals can move throughout the entire field of view (FOV). We developed a method to calculate the image-based resolution kernels of the motion dependent and spatially variant PSF (MD-SVPSF) to correct the loss of spatial resolution in motion corrected reconstructions. The resolution kernels are calculated for each voxel by sampling and averaging the SVPSF at all positions in the scanner FOV where the moving object was measured. In resolution phantom scans, the use of the MD-SVPSF resolution model improved the spatial resolution in motion corrected reconstructions and corrected the image deformation caused by the parallax effect consistently for all motion patterns, outperforming the use of a motion independent SVPSF or Gaussian kernels. Compared to motion correction in which the SVPSF is applied independently for every pose, our method performed similarly, but with more than two orders of magnitude faster computation time. Importantly, in scans of freely moving mice, brain regional quantification in motion-free and motion corrected images was better correlated when using the MD-SVPSF in comparison with motion independent SVPSF and a Gaussian kernel. The method developed here allows to obtain consistent spatial resolution and quantification in motion corrected images, independently of the motion pattern of the subject.

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.

A Higher-Order Polynomial Method for SPECT Reconstruction

Existing single-photon emission computed tomography (SPECT) reconstruction methods are mostly based on discrete models that may be viewed as piecewise constant approximations of a continuous data acquisition process. Due to low accuracy order of piecewise constant approximations, a traditional discrete model introduces irreducible model errors which are a bottleneck of the quality improvement of reconstructed images in clinical applications. To overcome this drawback, we develop a higher-order polynomial method for SPECT reconstruction. Specifically, we represent the data acquisition of SPECT imaging by using an integral equation model, approximate the solution of the underlying integral equation by higher-order piecewise polynomials leading to a new discrete system and introduce two novel regularizers for the system, by exploring the a priori knowledge of the radiotracer distribution, suitable for the approximation. The proposed higher-order polynomial method outperforms significantly the cutting edge reconstruction method based on a traditional discrete model in terms of model error reduction, noise suppression, and artifact reduction. In particular, the coefficient of variation of images reconstructed by the piecewise linear polynomial method is reduced by a factor of 10 in comparison to that of a traditional discrete model-based method.

Experimental validation of estimated spatially variant radioisotope-specific point spread functions using published positron range simulations and fluorine-18 measurements

In this work we compare spatially variant radioisotope-specific point spread functions (PSFs) derived from published positron range data with measured data using a high resolution research tomograph (HRRT). Spatially variant PSFs were measured on a HRRT for fluorine-18, carbon-11 and gallium-68 using an array of printed point sources. For gallium-68, this required modification of the original design to handle its longer positron range. Using the fluorine-18 measurements and previously published data from Monte-Carlo simulations of positron range, estimated PSFs for carbon-11 and gallium-68 were calculated and compared with experimental data. A double 3D Gaussian function was fitted to the estimated and measured data and used to model the spatially varying PSFs over the scanner field of view (FOV). Differences between the measured and estimated PSFs were quantified using the full-width-at-half-maximum (FWHM) and full-width-at-tenth-maximum (FWTM) in the tangential, radial and axial directions. While estimated PSFs were generally in agreement with the measured PSFs over the entire FOV better agreement was observed (FWHM and FWTM differences of less than 10%) when using one of the two sets of positron range simulations, especially for gallium-68 and for the FWTM. Spatially variant radioisotope specific PSFs can be accurately estimated from fluorine-18 measurements and published positron range data. We have experimentally validated this approach for carbon-11 and gallium-68, and such an approach may be applicable to other radioisotopes such as oxygen-15 for which measurements are not practical.

Sinogram Blurring Matrix Estimation From Point Sources Measurements With Rank-One Approximation for Fully 3-D PET

An accurate system matrix is essential in positron emission tomography (PET) for reconstructing high quality images. To reduce storage size and image reconstruction time, we factor the system matrix into a product of a geometry projection matrix and a sinogram blurring matrix. The geometric projection matrix is computed analytically and the sinogram blurring matrix is estimated from point source measurements. Previously, we have estimated a 2-D blurring matrix for a preclinical PET scanner. The 2-D blurring matrix only considers blurring effects within a transaxial sinogram and does not compensate for inter-sinogram blurring effects. For PET scanners with a long axial field of view, inter-sinogram blurring can be a major problem influencing the image quality in the axial direction. Hence, the estimation of a 4-D blurring matrix is desirable to further improve the image quality. The 4-D blurring matrix estimation is an ill-conditioned problem due to the large number of unknowns. Here, we propose a rank-one approximation for each blurring kernel image formed by a row vector of the sinogram blurring matrix to improve the stability of the 4-D blurring matrix estimation. The proposed method is applied to the simulated data as well as the real data obtained from an Inveon microPET scanner. The results show that the newly estimated 4-D blurring matrix can improve the image quality over those obtained with a 2-D blurring matrix and requires less point source scans to achieve similar image quality compared with an unconstrained 4-D blurring matrix estimation.

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.

A novel depth-of-interaction block detector for positron emission tomography using a dichotomous orthogonal symmetry decoding concept

Conventionally, a dual-end depth-of-interaction (DOI) block detector readout requires two two-dimensional silicon photomultiplier (SiPM) arrays, one on top and one on the bottom, to define the XYZ positions. However, because both the top and bottom SiPM arrays are reading the same pixels, this creates information redundancy. We propose a dichotomous orthogonal symmetric (DOS) dual-end readout block detector design, which removes this redundancy by reducing the number of SiPMs and still achieves XY and DOI (Z) decoding for positron emission tomography (PET) block detector. Reflecting films are used within the block detector to channel photons going to the top of the block to go only in the X direction, and photons going to the bottom are channeled along the Y direction. Despite the unidirectional channeling on each end, the top readout provides both X and Y information using two one-dimensional SiPM arrays instead of a two-dimensional SiPM array; similarly, the bottom readout also provides both X and Y information with just two one-dimensional SiPM arrays. Thus, a total of four one-dimensional SiPM arrays (4  ×  N SiPMs) are used to decode the XYZ positions of the firing pixels instead of two two-dimensional SiPM arrays (2  ×  N  ×  N SiPMs), reducing the number of SiPM arrays per block from 2N(2) to 4 N for PET/MR or PET/CT systems. Moreover, the SiPM arrays on one end can be replaced by two regular photomultiplier tubes (PMTs), so that a block needs only 2 N SiPMs  +  2 half-PMTs; this hybrid-DOS DOI block detector can be used in PET/CT systems. Monte Carlo simulations were carried out to study the performance of our DOS DOI block detector design, including the XY-decoding quality, energy resolution, and DOI resolution. Both BGO and LSO scintillators were studied. We found that 4 mm pixels were well decoded for 5  ×  5 BGO and 9  ×  9 LSO arrays with 4 to 5 mm DOI resolution and 16-20% energy resolution. By adding light-channel decoding, we modified the DOS design to a high-resolution design, which resolved scintillator pixels smaller than the SiPM dimensions. Detector pixels of 2.4 mm were decoded for 8  ×  8 BGO and 15  ×  15 LSO arrays with 5 mm DOI resolution and 20-23% energy resolution. Time performance was also studied for the 8  ×  8 BGO and 15  ×  15 LSO HR-DOS arrays. The timing resolution for the corner and central crystals is 986  ±  122 ps and 1.89  ±  0.17 μs respectively with BGO, 137  ±  42 ps and 458  ±  67 ps respectively with LSO. Monte Carlo simulations with GATE/Geant4 demonstrated the feasibility of our DOS DOI block detector design. In conclusion, our novel design achieved good performance except the time performance while using fewer SiPMs and supporting electronic channels than the current non-DOI PET detectors. This novel design can significantly reduce the cost, heat, and readout complexity of DOI block detectors for PET/MR/CT systems that don't require the time-of-flight capability.

Experimental evaluation and basis function optimization of the spatially variant image-space PSF on the Ingenuity PET/MR scanner

PURPOSE

The Ingenuity time-of-flight (TF) PET/MR is a recently developed hybrid scanner combining the molecular imaging capabilities of PET with the excellent soft tissue contrast of MRI. It is becoming common practice to characterize the system's point spread function (PSF) and understand its variation under spatial transformations to guide clinical studies and potentially use it within resolution recovery image reconstruction algorithms. Furthermore, due to the system's utilization of overlapping and spherical symmetric Kaiser-Bessel basis functions during image reconstruction, its image space PSF and reconstructed spatial resolution could be affected by the selection of the basis function parameters. Hence, a detailed investigation into the multidimensional basis function parameter space is needed to evaluate the impact of these parameters on spatial resolution.

METHODS

Using an array of 12 × 7 printed point sources, along with a custom made phantom, and with the MR magnet on, the system's spatially variant image-based PSF was characterized in detail. Moreover, basis function parameters were systematically varied during reconstruction (list-mode TF OSEM) to evaluate their impact on the reconstructed resolution and the image space PSF. Following the spatial resolution optimization, phantom, and clinical studies were subsequently reconstructed using representative basis function parameters.

RESULTS

Based on the analysis and under standard basis function parameters, the axial and tangential components of the PSF were found to be almost invariant under spatial transformations (~4 mm) while the radial component varied modestly from 4 to 6.7 mm. Using a systematic investigation into the basis function parameter space, the spatial resolution was found to degrade for basis functions with a large radius and small shape parameter. However, it was found that optimizing the spatial resolution in the reconstructed PET images, while having a good basis function superposition and keeping the image representation error to a minimum, is feasible, with the parameter combination range depending upon the scanner's intrinsic resolution characteristics.

CONCLUSIONS

Using the printed point source array as a MR compatible methodology for experimentally measuring the scanner's PSF, the system's spatially variant resolution properties were successfully evaluated in image space. Overall the PET subsystem exhibits excellent resolution characteristics mainly due to the fact that the raw data are not under-sampled/rebinned, enabling the spatial resolution to be dictated by the scanner's intrinsic resolution and the image reconstruction parameters. Due to the impact of these parameters on the resolution properties of the reconstructed images, the image space PSF varies both under spatial transformations and due to basis function parameter selection. Nonetheless, for a range of basis function parameters, the image space PSF remains unaffected, with the range depending on the scanner's intrinsic resolution properties.

Applications of the line-of-response probability density function resolution model in PET list mode reconstruction

Resolution degradation in PET image reconstruction can be caused by inaccurate modeling of the physical factors in the acquisition process. Resolution modeling (RM) is a common technique that takes into account the resolution degrading factors in the system matrix. Our previous work has introduced a probability density function (PDF) method of deriving the resolution kernels from Monte Carlo simulation and parameterizing the LORs to reduce the number of kernels needed for image reconstruction. In addition, LOR-PDF allows different PDFs to be applied to LORs from different crystal layer pairs of the HRRT. In this study, a thorough test was performed with this new model (LOR-PDF) applied to two PET scanners-the HRRT and Focus-220. A more uniform resolution distribution was observed in point source reconstructions by replacing the spatially-invariant kernels with the spatially-variant LOR-PDF. Specifically, from the center to the edge of radial field of view (FOV) of the HRRT, the measured in-plane FWHMs of point sources in a warm background varied slightly from 1.7 mm to 1.9 mm in LOR-PDF reconstructions. In Minihot and contrast phantom reconstructions, LOR-PDF resulted in up to 9% higher contrast at any given noise level than image-space resolution model. LOR-PDF also has the advantage in performing crystal-layer-dependent resolution modeling. The contrast improvement by using LOR-PDF was verified statistically by replicate reconstructions. In addition, [(11)C]AFM rats imaged on the HRRT and [(11)C]PHNO rats imaged on the Focus-220 were utilized to demonstrated the advantage of the new model. Higher contrast between high-uptake regions of only a few millimeter diameter and the background was observed in LOR-PDF reconstruction than in other methods.

Impact of point spread function modelling and time of flight on FDG uptake measurements in lung lesions using alternative filtering strategies

BACKGROUND

The use of maximum standardised uptake value (SUVmax) is commonplace in oncology positron emission tomography (PET). Point spread function (PSF) modelling and time-of-flight (TOF) reconstructions have a significant impact on SUVmax, presenting a challenge for centres with defined protocols for lesion classification based on SUVmax thresholds. This has perhaps led to the slow adoption of these reconstructions. This work evaluated the impact of PSF and/or TOF reconstructions on SUVmax, SUVpeak and total lesion glycolysis (TLG) under two different schemes of post-filtering.

METHODS

Post-filters to match voxel variance or SUVmax were determined using a NEMA NU-2 phantom. Images from 68 consecutive lung cancer patients were reconstructed with the standard iterative algorithm along with TOF; PSF modelling - Siemens HD·PET (HD); and combined PSF modelling and TOF - Siemens ultraHD·PET (UHD) with the two post-filter sets. SUVmax, SUVpeak, TLG and signal-to-noise ratio of tumour relative to liver (SNR(T-L)) were measured in 74 lesions for each reconstruction. Relative differences in uptake measures were calculated, and the clinical impact of any changes was assessed using published guidelines and local practice.

RESULTS

When matching voxel variance, SUVmax increased substantially (mean increase +32% and +49% for HD and UHD, respectively), potentially impacting outcome in the majority of patients. Increases in SUVpeak were less notable (mean increase +17% and +23% for HD and UHD, respectively). Increases with TOF alone were far less for both measures. Mean changes to TLG were <10% for all algorithms for either set of post-filters. SNR(T-L) were greater than ordered subset expectation maximisation (OSEM) in all reconstructions using both post-filtering sets.

CONCLUSIONS

Matching image voxel variance with PSF and/or TOF reconstructions, particularly with PSF modelling and in small lesions, resulted in considerable increases in SUVmax, inhibiting the use of defined protocols for lesion classification based on SUVmax. However, reduced partial volume effects may increase lesion detectability. Matching SUVmax in phantoms translated well to patient studies for PSF reconstruction but less well with TOF, where a small positive bias was observed in patient images. Matching SUVmax significantly reduced voxel variance and potential variability of uptake measures. Finally, TLG may be less sensitive to reconstruction methods compared with either SUVmax or SUVpeak.

A new PET resolution measurement method through Monte-Carlo simulations

OBJECTIVE

The aim of this study was to propose a novel method for image quality assessment in PET scanners through estimation of the modulation transfer function (MTF) of a plane source. The simulation was implemented using the previously validated Monte-Carlo model. A comparison of the proposed method with the more traditional technique, based on a line source, was also performed.

MATERIALS AND METHODS

The Geant4 application for tomographic emission (GATE) Monte-Carlo package was used for model development, and reconstructed images were obtained using software for tomographic image reconstruction (STIR) with cluster computing. A novel plane source consisting of a radioactive ((18)F-fluorodeoxyglucose) thin-layer chromatography plate was simulated (total source activity: 44.4 MBq) to assess image quality through the MTF. All images were reconstructed with the three-dimensional filtered back projection (FBP3DRP) and ordered-subsets expectation maximization (OSEM) reprojection algorithms.

RESULTS

The MTFs obtained using ordered-subsets expectation maximization show, in all cases, that higher frequencies are preserved compared with those obtained using the FBP3DRP. In addition, the plane source method is less prone to noise than the conventional line source method (SD=0.0031 and 0.0203, respectively).

CONCLUSION

The thin-layer chromatography-based plane source presented requires materials commonly found in a clinical environment and could be used to assess image quality in nuclear medicine departments and to further develop PET and single-photon emission computed tomography scanners through Monte-Carlo simulations.

Isotope specific resolution recovery image reconstruction in high resolution PET imaging

PURPOSE

Measuring and incorporating a scanner-specific point spread function (PSF) within image reconstruction has been shown to improve spatial resolution in PET. However, due to the short half-life of clinically used isotopes, other long-lived isotopes not used in clinical practice are used to perform the PSF measurements. As such, non-optimal PSF models that do not correspond to those needed for the data to be reconstructed are used within resolution modeling (RM) image reconstruction, usually underestimating the true PSF owing to the difference in positron range. In high resolution brain and preclinical imaging, this effect is of particular importance since the PSFs become more positron range limited and isotope-specific PSFs can help maximize the performance benefit from using resolution recovery image reconstruction algorithms.

METHODS

In this work, the authors used a printing technique to simultaneously measure multiple point sources on the High Resolution Research Tomograph (HRRT), and the authors demonstrated the feasibility of deriving isotope-dependent system matrices from fluorine-18 and carbon-11 point sources. Furthermore, the authors evaluated the impact of incorporating them within RM image reconstruction, using carbon-11 phantom and clinical datasets on the HRRT.

RESULTS

The results obtained using these two isotopes illustrate that even small differences in positron range can result in different PSF maps, leading to further improvements in contrast recovery when used in image reconstruction. The difference is more pronounced in the centre of the field-of-view where the full width at half maximum (FWHM) from the positron range has a larger contribution to the overall FWHM compared to the edge where the parallax error dominates the overall FWHM.

CONCLUSIONS

Based on the proposed methodology, measured isotope-specific and spatially variant PSFs can be reliably derived and used for improved spatial resolution and variance performance in resolution recovery image reconstruction. The benefits are expected to be more substantial for more energetic positron emitting isotopes such as Oxygen-15 and Rubidium-82.

Influence of the partial volume correction method on (18)F-fluorodeoxyglucose brain kinetic modelling from dynamic PET images reconstructed with resolution model based OSEM

Kinetic parameters estimated from dynamic (18)F-fluorodeoxyglucose ((18)F-FDG) PET acquisitions have been used frequently to assess brain function in humans. Neglecting partial volume correction (PVC) for a dynamic series has been shown to produce significant bias in model estimates. Accurate PVC requires a space-variant model describing the reconstructed image spatial point spread function (PSF) that accounts for resolution limitations, including non-uniformities across the field of view due to the parallax effect. For ordered subsets expectation maximization (OSEM), image resolution convergence is local and influenced significantly by the number of iterations, the count density, and background-to-target ratio. As both count density and background-to-target values for a brain structure can change during a dynamic scan, the local image resolution may also concurrently vary. When PVC is applied post-reconstruction the kinetic parameter estimates may be biased when neglecting the frame-dependent resolution. We explored the influence of the PVC method and implementation on kinetic parameters estimated by fitting (18)F-FDG dynamic data acquired on a dedicated brain PET scanner and reconstructed with and without PSF modelling in the OSEM algorithm. The performance of several PVC algorithms was quantified with a phantom experiment, an anthropomorphic Monte Carlo simulation, and a patient scan. Using the last frame reconstructed image only for regional spread function (RSF) generation, as opposed to computing RSFs for each frame independently, and applying perturbation geometric transfer matrix PVC with PSF based OSEM produced the lowest magnitude bias kinetic parameter estimates in most instances, although at the cost of increased noise compared to the PVC methods utilizing conventional OSEM. Use of the last frame RSFs for PVC with no PSF modelling in the OSEM algorithm produced the lowest bias in cerebral metabolic rate of glucose estimates, although by less than 5% in most cases compared to the other PVC methods. The results indicate that the PVC implementation and choice of PSF modelling in the reconstruction can significantly impact model parameters.

Noise propagation in resolution modeled PET imaging and its impact on detectability

Positron emission tomography imaging is affected by a number of resolution degrading phenomena, including positron range, photon non-collinearity and inter-crystal blurring. An approach to this issue is to model some or all of these effects within the image reconstruction task, referred to as resolution modeling (RM). This approach is commonly observed to yield images of higher resolution and subsequently contrast, and can be thought of as improving the modulation transfer function. Nonetheless, RM can substantially alter the noise distribution. In this work, we utilize noise propagation models in order to accurately characterize the noise texture of reconstructed images in the presence of RM. Furthermore we consider the task of lesion or defect detection, which is highly determined by the noise distribution as quantified using the noise power spectrum. Ultimately, we use this framework to demonstrate why conventional trade-off analyses (e.g. contrast versus noise, using simplistic noise metrics) do not provide a complete picture of the impact of RM and that improved performance of RM according to such analyses does not necessarily translate to the superiority of RM in detection task performance.

Accurate and efficient modeling of the detector response in small animal multi-head PET systems

In fully three-dimensional PET imaging, iterative image reconstruction techniques usually outperform analytical algorithms in terms of image quality provided that an appropriate system model is used. In this study we concentrate on the calculation of an accurate system model for the YAP-(S)PET II small animal scanner, with the aim to obtain fully resolution- and contrast-recovered images at low levels of image roughness. For this purpose we calculate the system model by decomposing it into a product of five matrices: (1) a detector response component obtained via Monte Carlo simulations, (2) a geometric component which describes the scanner geometry and which is calculated via a multi-ray method, (3) a detector normalization component derived from the acquisition of a planar source, (4) a photon attenuation component calculated from x-ray computed tomography data, and finally, (5) a positron range component is formally included. This system model factorization allows the optimization of each component in terms of computation time, storage requirements and accuracy. The main contribution of this work is a new, efficient way to calculate the detector response component for rotating, planar detectors, that consists of a GEANT4 based simulation of a subset of lines of flight (LOFs) for a single detector head whereas the missing LOFs are obtained by using intrinsic detector symmetries. Additionally, we introduce and analyze a probability threshold for matrix elements of the detector component to optimize the trade-off between the matrix size in terms of non-zero elements and the resulting quality of the reconstructed images. In order to evaluate our proposed system model we reconstructed various images of objects, acquired according to the NEMA NU 4-2008 standard, and we compared them to the images reconstructed with two other system models: a model that does not include any detector response component and a model that approximates analytically the depth of interaction as detector response component. The comparisons confirm previous research results, showing that the usage of an accurate system model with a realistic detector response leads to reconstructed images with better resolution and contrast recovery at low levels of image roughness.

Acceleration of image-based resolution modelling reconstruction using an expectation maximization nested algorithm

Recent studies have demonstrated the benefits of a resolution model within iterative reconstruction algorithms in an attempt to account for effects that degrade the spatial resolution of the reconstructed images. However, these algorithms suffer from slower convergence rates, compared to algorithms where no resolution model is used, due to the additional need to solve an image deconvolution problem. In this paper, a recently proposed algorithm, which decouples the tomographic and image deconvolution problems within an image-based expectation maximization (EM) framework, was evaluated. This separation is convenient, because more computational effort can be placed on the image deconvolution problem and therefore accelerate convergence. Since the computational cost of solving the image deconvolution problem is relatively small, multiple image-based EM iterations do not significantly increase the overall reconstruction time. The proposed algorithm was evaluated using 2D simulations, as well as measured 3D data acquired on the high-resolution research tomograph. Results showed that bias reduction can be accelerated by interleaving multiple iterations of the image-based EM algorithm solving the resolution model problem, with a single EM iteration solving the tomographic problem. Significant improvements were observed particularly for voxels that were located on the boundaries between regions of high contrast within the object being imaged and for small regions of interest, where resolution recovery is usually more challenging. Minor differences were observed using the proposed nested algorithm, compared to the single iteration normally performed, when an optimal number of iterations are performed for each algorithm. However, using the proposed nested approach convergence is significantly accelerated enabling reconstruction using far fewer tomographic iterations (up to 70% fewer iterations for small regions). Nevertheless, the optimal number of nested image-based EM iterations is hard to be defined and it should be selected according to the given application.

Resolution modeling in PET imaging: theory, practice, benefits, and pitfalls

In this paper, the authors review the field of resolution modeling in positron emission tomography (PET) image reconstruction, also referred to as point-spread-function modeling. The review includes theoretical analysis of the resolution modeling framework as well as an overview of various approaches in the literature. It also discusses potential advantages gained via this approach, as discussed with reference to various metrics and tasks, including lesion detection observer studies. Furthermore, attention is paid to issues arising from this approach including the pervasive problem of edge artifacts, as well as explanation and potential remedies for this phenomenon. Furthermore, the authors emphasize limitations encountered in the context of quantitative PET imaging, wherein increased intervoxel correlations due to resolution modeling can lead to significant loss of precision (reproducibility) for small regions of interest, which can be a considerable pitfall depending on the task of interest.

High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations.

Fast and efficient fully 3D PET image reconstruction using sparse system matrix factorization with GPU acceleration

Statistically based iterative image reconstruction has been widely used in positron emission tomography (PET) imaging. The quality of reconstructed images depends on the accuracy of the system matrix that defines the mapping from the image space to the data space. However, an accurate system matrix is often associated with high computation cost and huge storage requirement. In this paper, we present a method to address this problem using sparse matrix factorization and graphics processor unit (GPU) acceleration. We factor the accurate system matrix into three highly sparse matrices: a sinogram blurring matrix, a geometric projection matrix and an image blurring matrix. The geometrical projection matrix is precomputed based on a simple line integral model, while the sinogram and image blurring matrices are estimated from point-source measurements. The resulting factored system matrix has far less nonzero elements than the original system matrix, which substantially reduces the storage and computation cost. The smaller matrix size also allows an efficient implementation of the forward and backward projectors on a GPU, which often has a limited memory space. Our experimental studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction, while achieving better performance than existing factorization methods.