Fast, accurate and shift-varying line projections for iterative reconstruction using the GPU

Initial demonstration of the Scratch-PET concept: an intraoperative PET with a hand-held detector

Positron emission tomography (PET) is a valuable tool for diagnosing malignant tumors. Intraoperative PET imaging is expected to allow the more accurate localization of tumors that need resections. However, conventional devices feature a large detector ring that obstructs surgical procedures, preventing their intraoperative application. This paper proposes a new PET device, Scratch-PET, for image-guided tumor resection. The key feature of Scratch-PET is its use of a hand-held detector to scan the surgical field, ensuring open space for surgery while measuring annihilation radiation with a fixed detector array placed below the patient. We developed a prototype device using two detectors: the hand-held detector and a fixed detector, to demonstrate the feasibility of the proposed concept. Both detectors consisted of 16 × 16 arrays of lutetium yttrium orthosilicates (3 × 3 × 15 mm3) coupled one-to-one with 16 × 16 silicon photomultiplier arrays. The position and orientation of the hand-held detector are tracked using an optical tracking sensor that detects attached markers. We measured a 22Na multi-rod phantom and two 22Na point sources separately for 180 s while moving the hand-held detector. The rod diameters were 6.0, 5.0, 4.0, 3.0, 2.2, and 1.6 mm. Each point source was placed at the field-of-view center and 35 mm off-center which was outside the sensitive area when the hand-held detector was positioned facing the fixed detector. The 2.2 mm rods were partially resolved, and both point sources were successfully visualized. The potential of the proposed device to visualize small tumors was validated.

A modified orthogonal-distance ray-tracer method applied to dual rotation PET systems

Objective.a new projector, orthogonal-distance ray-tracer varying-full width at half maximum (OD-RT-VF), was developed to model a shift-variant elliptical point-spread function (PSF) response to improve the image quality (IQ) of a preclinical dual-rotation PET system.Approach.the OD-RT-VF projector models different FWHM values of the PSF in multiple directions, using half-height and half-width tube-of-response (ToR) values. The OD-RT-VF method's performance was evaluated against the original OD-RT method and a ToR model with constant response. The evaluation involved simulations of NEMA NU 4-2008 IQ and Derenzo phantoms, as well as a real mouse injected with [18F]-NaF scanned with the easyPET.3D system.Main results.the OD-RT-VF method demonstrated superior image resolution and uniformity (11.9% vs 15.9%) compared to the OD-RT model. In micro-derenzo phantom simulations, it resolved rods down to 1.0 mm, outperforming the other methods. For IQ phantom simulations, the OD-RT-VF projector at convergency achieved hot rods recovery coefficients ranging from 22.4% to 93.3% and lower spillover ratios in cold regions of 0.22 and 0.33 for air and water, respectively. For bone radiotracer imaging, OD-RT-VF produced clearer images of major skeletal parts, with less noise compared to OD-RT and better resolution compared to ToR projectors.Significance.the study shows that the OD-RT-VF projector method enhances PET imaging by providing better resolution, uniformity, and IQ. This model, in addition to a list-mode and GPU-based reconstruction addressing the data sparsity of dual-rotation PET geometries, unlocks their imaging potential for small animal imaging.

PARALLELPROJ-an open-source framework for fast calculation of projections in tomography

In this article, we introduce parallelproj, a novel open-source framework designed for efficient parallel computation of projections in tomography leveraging either multiple CPU cores or GPUs. This framework efficiently implements forward and back projection functions for both sinogram and listmode data, utilizing Joseph's method, which is further extended to encompass time-of-flight (TOF) PET projections. Our evaluation involves a series of tests focusing on PET image reconstruction using data sourced from a state-of-the-art clinical PET/CT system. We thoroughly benchmark the performance of the projectors in non-TOF and TOF, sinogram, and listmode employing multi CPU-cores, hybrid CPU/GPU, and exclusive GPU mode. Moreover, we also investigate the timing of non-TOF sinogram projections calculated in STIR (Software for Tomographic Image Reconstruction) which recently integrated parallelproj as one of its projection backends. Our results indicate that the exclusive GPU mode provides acceleration factors between 25 and 68 relative to the multi-CPU-core mode. Furthermore, we demonstrate that OSEM listmode reconstruction of state-of-the-art real-world PET data sets is achievable within a few seconds using a single consumer GPU.

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.

Optimization of Spatial Resolution and Image Reconstruction Parameters for the Small-Animal Metis™ PET/CT System

Purpose: The aim of this study was to investigate the optimization of the spatial resolution and image reconstruction parameters related to image quality in an iterative reconstruction algorithm for the small-animal Metis™ PET/CT system. Methods: We used a homemade Derenzo phantom to evaluate the image quality using visual assessment, the signal-to-noise ratio, the contrast, the coefficient of variation, and the contrast-to-noise ratio of the 0.8 mm hot rods of eight slices in the center of the phantom PET images. A healthy mouse study was performed to analyze the influence of the optimal reconstruction parameters and the Gaussian post-filter FWHM. Results: In the phantom study, the image quality was the best when the phantom was placed at the end, keeping the central axis parallel to the X-axis of the system, and selecting between 30 and 40 iterations, a 0.314 mm reconstructed voxel size, and a 1.57 mm Gaussian post-filter FWHM. The optimization of the spatial resolution could reach 0.6 mm. In the animal study, it was suitable to choose a voxel size of 0.472 mm, between 30 and 40 iterations, and a 2.36 mm Gaussian post-filter FWHM. Conclusions: Our results indicate that the optimal imaging conditions and reconstruction parameters are very necessary to obtain high-resolution images and quantitative accuracy, especially for the high-precision recognition of tiny lesions.

Cycle-consistent learning-based hybrid iterative reconstruction for whole-body PET imaging

Objective. To develop a cycle-consistent learning-based hybrid iterative reconstruction (IR) method that takes only slightly longer than analytic reconstruction, while pursuing the image resolution and tumor quantification achievable by IR for whole-body PET imaging. Approach. We backproject the raw positron emission tomography (PET) data to generate a blurred activity distribution. From the backprojection to the IR label, a reconstruction mapping that approximates the deblurring filters for the point spread function and the physical effects of the PET system is unrolled to a neural network with stacked convolutional layers. By minimizing the cycle-consistent loss, we train the reconstruction and inverse mappings simultaneously. Main results. In phantom study, the proposed method results in an absolute relative error (RE) of the mean activity of 4.0% ± 0.7% in the largest hot sphere, similar to the RE of the full-count IR and significantly smaller than that obtained by CycleGAN postprocessing. Achieving a noise reduction of 48.1% ± 0.5% relative to the low-count IR, the proposed method demonstrates advantages over the low-count IR and CycleGAN in terms of resolution maintenance, contrast recovery, and noise reduction. In patient study, the proposed method obtains a noise reduction of 44.6% ± 8.0% for the lung and the liver, while maintaining the regional mean activity in both simulated lesions and real tumors. The run time of the proposed method is only half that of the conventional IR. Significance. The proposed cycle-consistent learning from the backprojection rather than the raw PET data or an IR result enables improved reconstruction accuracy, reduced memory requirements, and fast implementation speeds for clinical whole-body PET imaging.

Augmented Whole-Body Scanning via Magnifying PET

A novel technique, called augmented whole-body scanning via magnifying PET (AWSM-PET), that improves the sensitivity and lesion detectability of a PET scanner for whole-body imaging is proposed and evaluated. A Siemens Biograph Vision PET/CT scanner equipped with one or two high-resolution panel-detectors was simulated to study the effectiveness of AWSM-PET technology. The detector panels are located immediately outside the scanner's axial field-of-view (FOV). A detector panel contains 2 ×8 detector modules each consisting of 32 ×64 LSO crystals ( 1.0 ×1.0 ×10.0 mm3 each). A 22Na point source was stepped across the scanner's FOV axially to measure sensitivity profiles at different locations. An elliptical torso phantom containing 7×9 spherical lesions was imaged at different axial locations to mimic a multi-bed-position whole-body imaging protocol. Receiver operating characteristic (ROC) curves were analyzed to evaluate the improvement in lesion detectability by the AWSM-PET technology. Experimental validation was conducted using an existing flat-panel detector integrated with a Siemens Biograph 40 PET/CT scanner to image a torso phantom containing spherical lesions with diameters ranging from 3.3 to 11.4 mm. The contrast-recovery-coefficient (CRC) of the lesions was evaluated for the scanner with or without the AWSM-PET technology. Monte Carlo simulation shows 36%-42% improvement in system sensitivity by a dual-panel AWSM-PET device. The area under the ROC curve is 0.962 by a native scanner for the detection of 4 mm diameter lesions with 5:1 tumor-to-background activity concentration. It was improved to 0.977 and 0.991 with a single- and dual-panel AWSM-PET system, respectively. Experimental studies showed that the average CRC of 3.3 mm and 4.3 mm diameter tumors were improved from 2.8% and 4.2% to 7.9% and 11.0%, respectively, by a single-panel AWSM-PET device. With a high-sensitivity dual-panel device, the corresponding CRC can be further improved to 11.0% and 15.9%, respectively. The principle of the AWSM-PET technology has been developed and validated. Enhanced system sensitivity, CRC and tumor detectability were demonstrated by Monte Carlo simulations and imaging experiments. This technology may offer a cost-effective path to realize high-resolution whole-body PET imaging clinically.

Penalized maximum-likelihood reconstruction for improving limited-angle artifacts in a dedicated head and neck PET system

Positron emission tomography (PET) suffers from limited spatial resolution in current head and neck cancer management. We are building a dual-panel high-resolution PET system to aid the detection of tumor involvement in small lymph nodes ([Formula: see text]10 mm in diameter). The system is based on cadmium zinc telluride (CZT) detectors with cross-strip electrode readout (1 mm anode pitch and 5 mm cathode pitch). One challenge of the dual-panel system is that the limited angular coverage of the imaging volume leads to artifacts in reconstructed images, such as the elongation of lesions. In this work, we leverage a penalized maximum-likelihood (PML) reconstruction for the limited-angle PET system. The dissimilarity between the image to be reconstructed and a prior image from a low-resolution whole-body scanner is penalized. An image-based resolution model is incorporated into the regularization. Computer simulations were used to evaluate the performance of the method. Results demonstrate that the elongation of the 6-mm and 8-mm diameter hot spheres is eliminated with the regularization strength γ being 0.02 or larger. The PML reconstruction yields higher contrast recovery coefficient (CRC) of hot spheres compared to the maximum-likelihood reconstruction, as well as the low-resolution whole-body image, across all hot sphere sizes tested (3, 4, 6, and 8 mm). The method studied in this work provides a way to mitigate the limited-angle artifacts in the reconstruction from limited-angle PET data, making the high-resolution dual-panel dedicated head and neck PET system promising for head and neck cancer management.

Real-Time 3D PET Image with Pseudoinverse Reconstruction

Real-time positron emission tomography (PET) may provide information from first-shot images, enable PET-guided biopsies, and allow awake animal studies. Fully-3D iterative reconstructions yield the best images in PET, but they are too slow for real-time imaging. Analytical methods such as Fourier back projection (FBP) are very fast, but yield images of poor quality with artifacts due to noise or data incompleteness. In this work, an image reconstruction based on the pseudoinverse of the system response matrix (SRM) is presented. w. To implement the pseudoinverse method, the reconstruction problem is separated into two stages. First, the axial part of the SRM is pseudo-inverted (PINV) to rebin the 3D data into 2D datasets. Then, the resulting 2D slices can be reconstructed with analytical methods or by applying the pseudoinverse algorithm again. The proposed two-step PINV reconstruction yielded good-quality images at a rate of several frames per second, compatible with real time applications. Furthermore, extremely fast direct PINV reconstruction of projections of the 3D image collapsed along specific directions can be implemented.

Real-Time 3D PET Image with Pseudoinverse Reconstruction

Real-time positron emission tomography (PET) may provide information from first-shot images, enable PET-guided biopsies, and allow awake animal studies. Fully-3D iterative reconstructions yield the best images in PET, but they are too slow for real-time imaging. Analytical methods such as Fourier back projection (FBP) are very fast, but yield images of poor quality with artifacts due to noise or data incompleteness. In this work, an image reconstruction based on the pseudoinverse of the system response matrix (SRM) is presented. w. To implement the pseudoinverse method, the reconstruction problem is separated into two stages. First, the axial part of the SRM is pseudo-inverted (PINV) to rebin the 3D data into 2D datasets. Then, the resulting 2D slices can be reconstructed with analytical methods or by applying the pseudoinverse algorithm again. The proposed two-step PINV reconstruction yielded good-quality images at a rate of several frames per second, compatible with real time applications. Furthermore, extremely fast direct PINV reconstruction of projections of the 3D image collapsed along specific directions can be implemented.

An automatic algorithm to exploit the symmetries of the system response matrix in positron emission tomography iterative reconstruction

Positron emission tomography (PET) iterative 3D reconstruction is a very computational demanding task. One of the main issues of the iterative reconstruction concerns the management of the system response matrix (SRM). The SRM models the relationship between the projection and the voxel space and its memory footprint can easily exceed hundreds of GB. Moreover, in order to make the reconstruction fast enough not to hinder its practical application, the SRM must be stored in the random access memory of the workstation used for the reconstruction. This issue is normally solved by implementing efficient storage schemes and by reducing the number of redundant patterns in the SRM through symmetries. However, finding a sufficient number of symmetries is often non-trivial and is typically performed using dedicated solutions that cannot be exported to different detectors and geometries. In this paper, an automatic approach to reduce the memory footprint of a pre-computed SRM is described. The proposed approach was named symmetry search algorithm (SSA) and consists in an algorithm that searches for some of the redundant patterns present in the SRM, leading to its lossy compression. This approach was built to detect translations, reflections and coordinates swap in voxel space. Therefore, it is particularly well suited for those scanners where some of the rotational symmetries are broken, e.g. small animal scanner where the modules are arranged in a polygonal ring made of few elements, and dual head planar PET systems. In order to validate this approach, the SSA is applied to the SRM of a preclinical scanner (the IRIS PET/CT). The data acquired by the scanner were reconstructed with a dedicated maximum likelihood estimation maximization algorithm with both the uncompressed and the compressed SRMs. The results achieved show that the information lost due to the SSA compression is negligible. Compression factors up to 52 when using the SSA together with manually inserted symmetries and up to 204 when using the SSA alone, can be obtained for the IRIS SRM. These results come without significant differences in the values and in the main quality metrics of the reconstructed images, i.e. spatial resolution and noise. Although the compression factors depend on the system considered, the SSA is applicable to any SRM and therefore it can be considered a general tool to reduce the footprint of a pre-computed SRM.

Implementation of GPU accelerated SPECT reconstruction with Monte Carlo-based scatter correction

OBJECTIVE

Statistical SPECT reconstruction can be very time-consuming especially when compensations for collimator and detector response, attenuation, and scatter are included in the reconstruction. This work proposes an accelerated SPECT reconstruction algorithm based on graphics processing unit (GPU) processing.

METHODS

Ordered subset expectation maximization (OSEM) algorithm with CT-based attenuation modelling, depth-dependent Gaussian convolution-based collimator-detector response modelling, and Monte Carlo-based scatter compensation was implemented using OpenCL. The OpenCL implementation was compared against the existing multi-threaded OSEM implementation running on a central processing unit (CPU) in terms of scatter-to-primary ratios, standardized uptake values (SUVs), and processing speed using mathematical phantoms and clinical multi-bed bone SPECT/CT studies.

RESULTS

The difference in scatter-to-primary ratios, visual appearance, and SUVs between GPU and CPU implementations was minor. On the other hand, at its best, the GPU implementation was noticed to be 24 times faster than the multi-threaded CPU version on a normal 128 × 128 matrix size 3 bed bone SPECT/CT data set when compensations for collimator and detector response, attenuation, and scatter were included.

CONCLUSIONS

GPU SPECT reconstructions show great promise as an every day clinical reconstruction tool.

Sparse domain approaches in dynamic SPECT imaging with high-performance computing

Iterative reconstruction algorithms often have relatively large computation time affecting their clinical deployment. This is especially true for 4D reconstruction in dynamic imaging (DI). In this work, we have shown how sparse domain approaches and parallelization for static 3D image reconstruction and 4D dynamic image reconstruction (directly from sinogram) in Single Photon Emission Computed Tomography (SPECT), without any intermediate 3D reconstructions, can improve computational efficiency. DI in SPECT is one of the hardest inverse problems in medical image reconstruction area and slow reconstruction is a challenge for this promising protocol. Our work hopefully, paves a new direction toward making DI in SPECT clinically viable. Our 4D reconstruction also is a novel application of non-negative matrix factorization (NNMF) in an inverse problem.

A review of GPU-based medical image reconstruction

Tomographic image reconstruction is a computationally demanding task, even more so when advanced models are used to describe a more complete and accurate picture of the image formation process. Such advanced modeling and reconstruction algorithms can lead to better images, often with less dose, but at the price of long calculation times that are hardly compatible with clinical workflows. Fortunately, reconstruction tasks can often be executed advantageously on Graphics Processing Units (GPUs), which are exploited as massively parallel computational engines. This review paper focuses on recent developments made in GPU-based medical image reconstruction, from a CT, PET, SPECT, MRI and US perspective. Strategies and approaches to get the most out of GPUs in image reconstruction are presented as well as innovative applications arising from an increased computing capacity. The future of GPU-based image reconstruction is also envisioned, based on current trends in high-performance computing.

Study of material properties important for an optical property modulation-based radiation detection method for positron emission tomography

We compare the performance of two detector materials, cadmium telluride (CdTe) and bismuth silicon oxide (BSO), for optical property modulation-based radiation detection method for positron emission tomography (PET), which is a potential new direction to dramatically improve the annihilation photon pair coincidence time resolution. We have shown that the induced current flow in the detector crystal resulting from ionizing radiation determines the strength of optical modulation signal. A larger resistivity is favorable for reducing the dark current (noise) in the detector crystal, and thus the higher resistivity BSO crystal has a lower (50% lower on average) noise level than CdTe. The CdTe and BSO crystals can achieve the same sensitivity under laser diode illumination at the same crystal bias voltage condition while the BSO crystal is not as sensitive to 511-keV photons as the CdTe crystal under the same crystal bias voltage. The amplitude of the modulation signal induced by 511-keV photons in BSO crystal is around 30% of that induced in CdTe crystal under the same bias condition. In addition, we have found that the optical modulation strength increases linearly with crystal bias voltage before saturation. The modulation signal with CdTe tends to saturate at bias voltages higher than 1500 V due to its lower resistivity (thus larger dark current) while the modulation signal strength with BSO still increases after 3500 V. Further increasing the bias voltage for BSO could potentially further enhance the modulation strength and thus, the sensitivity.

Trace: a high-throughput tomographic reconstruction engine for large-scale datasets

BACKGROUND

Modern synchrotron light sources and detectors produce data at such scale and complexity that large-scale computation is required to unleash their full power. One of the widely used imaging techniques that generates data at tens of gigabytes per second is computed tomography (CT). Although CT experiments result in rapid data generation, the analysis and reconstruction of the collected data may require hours or even days of computation time with a medium-sized workstation, which hinders the scientific progress that relies on the results of analysis.

METHODS

We present Trace, a data-intensive computing engine that we have developed to enable high-performance implementation of iterative tomographic reconstruction algorithms for parallel computers. Trace provides fine-grained reconstruction of tomography datasets using both (thread-level) shared memory and (process-level) distributed memory parallelization. Trace utilizes a special data structure called replicated reconstruction object to maximize application performance. We also present the optimizations that we apply to the replicated reconstruction objects and evaluate them using tomography datasets collected at the Advanced Photon Source.

RESULTS

Our experimental evaluations show that our optimizations and parallelization techniques can provide 158× speedup using 32 compute nodes (384 cores) over a single-core configuration and decrease the end-to-end processing time of a large sinogram (with 4501 × 1 × 22,400 dimensions) from 12.5 h to <5 min per iteration.

CONCLUSION

The proposed tomographic reconstruction engine can efficiently process large-scale tomographic data using many compute nodes and minimize reconstruction times.

Feasibility study of Compton cameras for x-ray fluorescence computed tomography with humans

X-ray fluorescence imaging is a promising imaging technique able to depict the spatial distributions of low amounts of molecular agents in vivo. Currently, the translation of the technique to preclinical and clinical applications is hindered by long scanning times as objects are scanned with flux-limited narrow pencil beams. The study presents a novel imaging approach combining x-ray fluorescence imaging with Compton imaging. Compton cameras leverage the imaging performance of XFCT and abolish the need for pencil beam excitation. The study examines the potential of this new imaging approach on the base of Monte-Carlo simulations. In the work, it is first presented that the particular option of slice/fan-beam x-ray excitation has advantages in image reconstruction in regard of processing time and image quality compared to traditional volumetric Compton imaging. In a second experiment, the feasibility of the approach for clinical applications with tracer agents made from gold nano-particles is examined in a simulated lung scan scenario. The high energy of characteristic x-ray photons from gold is advantageous for deep tissue penetration and has lower angular blurring in the Compton camera. It is found that Doppler broadening in the first detector stage of the Compton camera adds the largest contribution on the angular blurring; physically limiting the spatial resolution. Following the analysis of the results from the spatial resolution test, resolutions in the order of one centimeter are achievable with the approach in the center of the lung. The concept of Compton imaging allows one to distinguish to some extent between scattered photons and x-ray fluorescent photons based on their difference in emission position. The results predict that molecular sensitivities down to 240 pM l^-1 for 5 mm diameter lesions at 15 mGy for 50 nm diameter gold nano-particles are achievable. A 45-fold speed up time for data acquisition compared to traditional pencil beam XFCT could be achieved for lung imaging at the cost of a small sensitivity decrease.

Dynamic PET reconstruction using temporal patch-based low rank penalty for ROI-based brain kinetic analysis

Dynamic positron emission tomography (PET) is widely used to measure changes in the bio-distribution of radiopharmaceuticals within particular organs of interest over time. However, to retain sufficient temporal resolution, the number of photon counts in each time frame must be limited. Therefore, conventional reconstruction algorithms such as the ordered subset expectation maximization (OSEM) produce noisy reconstruction images, thus degrading the quality of the extracted time activity curves (TACs). To address this issue, many advanced reconstruction algorithms have been developed using various spatio-temporal regularizations. In this paper, we extend earlier results and develop a novel temporal regularization, which exploits the self-similarity of patches that are collected in dynamic images. The main contribution of this paper is to demonstrate that the correlation of patches can be exploited using a low-rank constraint that is insensitive to global intensity variations. The resulting optimization framework is, however, non-Lipschitz and nonconvex due to the Poisson log-likelihood and low-rank penalty terms. Direct application of the conventional Poisson image deconvolution by an augmented Lagrangian (PIDAL) algorithm is, however, problematic due to its large memory requirements, which prevents its parallelization. Thus, we propose a novel optimization framework using the concave-convex procedure (CCCP)

Efficient system modeling for a small animal PET scanner with tapered DOI detectors

A prototype small animal positron emission tomography (PET) scanner for mouse brain imaging has been developed at UC Davis. The new scanner uses tapered detector arrays with depth of interaction (DOI) measurement. In this paper, we present an efficient system model for the tapered PET scanner using matrix factorization and a virtual scanner geometry. The factored system matrix mainly consists of two components: a sinogram blurring matrix and a geometrical matrix. The geometric matrix is based on a virtual scanner geometry. The sinogram blurring matrix is estimated by matrix factorization. We investigate the performance of different virtual scanner geometries. Both simulation study and real data experiments are performed in the fully 3D mode to study the image quality under different system models. The results indicate that the proposed matrix factorization can maintain image quality while substantially reduce the image reconstruction time and system matrix storage cost. The proposed method can be also applied to other PET scanners with DOI measurement.

An Effective CUDA Parallelization of Projection in Iterative Tomography Reconstruction

Projection and back-projection are the most computationally intensive parts in Computed Tomography (CT) reconstruction, and are essential to acceleration of CT reconstruction algorithms. Compared to back-projection, parallelization efficiency in projection is highly limited by racing condition and thread unsynchronization. In this paper, a strategy of Fixed Sampling Number Projection (FSNP) is proposed to ensure the operation synchronization in the ray-driven projection with Graphical Processing Unit (GPU). Texture fetching is also used utilized to further accelerate the interpolations in both projection and back-projection. We validate the performance of this FSNP approach using both simulated and real cone-beam CT data. Experimental results show that compare to the conventional approach, the proposed FSNP method together with texture fetching is 10~16 times faster than the conventional approach based on global memory, and thus leads to more efficient iterative algorithm in CT reconstruction.

Iterative reconstruction of CT images on GPUs

Although widely used in nuclear medicine (gamma-camera, single photon emission computed tomography (SPECT), positron emission tomography (PET)), iterative reconstruction has not yet penetrated in CT. The main reason for this is that data sets in CT are much larger than in nuclear medicine and iterative reconstruction then becomes computationally very intensive. Graphical Processing Units (GPUs) provide the possibility to reduce effectively the high computational cost of their implementation. It is the goal of this work to develop a GPU-based algorithm to reconstruct high quality images from under sampled and noisy projection data.

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.

Relative role of motion and PSF compensation in whole-body oncologic PET-MR imaging

PURPOSE

Respiratory motion and partial-volume effects are the two main sources of image degradation in whole-body PET imaging. Simultaneous PET-MR allows measurement of respiratory motion using MRI while collecting PET events. Improved PET images may be obtained by modeling respiratory motion and point spread function (PSF) within the PET iterative reconstruction process. In this study, the authors assessed the relative impact of PSF modeling and MR-based respiratory motion correction in phantoms and patient studies using a whole-body PET-MR scanner.

METHODS

An asymmetric exponential PSF model accounting for radially varying and axial detector blurring effects was obtained from point source acquisitions performed in the PET-MR scanner. A dedicated MRI acquisition protocol using single-slice steady state free-precession MR acquisitions interleaved with pencil-beam navigator echoes was developed to track respiratory motion during PET-MR studies. An iterative ordinary Poisson fully 3D OSEM PET reconstruction algorithm modeling all the physical effects of the acquisition (attenuation, scatters, random events, detectors efficiencies, PSF), as well as MR-based nonrigid respiratory deformations of tissues (in both emission and attenuation maps) was developed. Phantom and(18)F-FDG PET-MR patient studies were performed to evaluate the proposed quantitative PET-MR methods.

RESULTS

The phantom experiment results showed that PSF modeling significantly improved contrast recovery while limiting noise propagation in the reconstruction process. In patients with soft-tissue static lesions, PSF modeling improved lesion contrast by 19.7%-109%, enhancing the detectability and assessment of small tumor foci. In a patient study with small moving hepatic lesions, the proposed reconstruction technique improved lesion contrast by 54.4%-98.1% and reduced apparent lesion size by 21.8%-34.2%. Improvements were particularly important for the smallest lesion undergoing large motion at the lung-liver interface. Heterogeneous tumor structures delineation was substantially improved. Enhancements offered by PSF modeling were more important when correcting for motion at the same time.

CONCLUSIONS

The results suggest that the proposed quantitative PET-MR methods can significantly enhance the performance of tumor diagnosis and staging as compared to conventional methods. This approach may enable utilization of the full potential of the scanner in oncologic studies of both the lower abdomen, with moving lesions, as well as other parts of the body unaffected by motion.

MAP reconstruction for Fourier rebinned TOF-PET data

Time-of-flight (TOF) information improves the signal-to-noise ratio in positron emission tomography (PET). The computation cost in processing TOF-PET sinograms is substantially higher than for nonTOF data because the data in each line of response is divided among multiple TOF bins. This additional cost has motivated research into methods for rebinning TOF data into lower dimensional representations that exploit redundancies inherent in TOF data. We have previously developed approximate Fourier methods that rebin TOF data into either three-dimensional (3D) nonTOF or 2D nonTOF formats. We refer to these methods respectively as FORET-3D and FORET-2D. Here we describe maximum a posteriori (MAP) estimators for use with FORET rebinned data. We first derive approximate expressions for the variance of the rebinned data. We then use these results to rescale the data so that the variance and mean are approximately equal allowing us to use the Poisson likelihood model for MAP reconstruction. MAP reconstruction from these rebinned data uses a system matrix in which the detector response model accounts for the effects of rebinning. Using these methods we compare the performance of FORET-2D and 3D with TOF and nonTOF reconstructions using phantom and clinical data. Our phantom results show a small loss in contrast recovery at matched noise levels using FORET compared to reconstruction from the original TOF data. Clinical examples show FORET images that are qualitatively similar to those obtained from the original TOF-PET data but with a small increase in variance at matched resolution. Reconstruction time is reduced by a factor of 5 and 30 using FORET3D+MAP and FORET2D+MAP respectively compared to 3D TOF MAP, which makes these methods attractive for clinical applications.

Medical image processing on the GPU - past, present and future

Graphics processing units (GPUs) are used today in a wide range of applications, mainly because they can dramatically accelerate parallel computing, are affordable and energy efficient. In the field of medical imaging, GPUs are in some cases crucial for enabling practical use of computationally demanding algorithms. This review presents the past and present work on GPU accelerated medical image processing, and is meant to serve as an overview and introduction to existing GPU implementations. The review covers GPU acceleration of basic image processing operations (filtering, interpolation, histogram estimation and distance transforms), the most commonly used algorithms in medical imaging (image registration, image segmentation and image denoising) and algorithms that are specific to individual modalities (CT, PET, SPECT, MRI, fMRI, DTI, ultrasound, optical imaging and microscopy). The review ends by highlighting some future possibilities and challenges.

Distributed MLEM: an iterative tomographic image reconstruction algorithm for distributed memory architectures

The processing speed for positron emission tomography (PET) image reconstruction has been greatly improved in recent years by simply dividing the workload to multiple processors of a graphics processing unit (GPU). However, if this strategy is generalized to a multi-GPU cluster, the processing speed does not improve linearly with the number of GPUs. This is because large data transfer is required between the GPUs after each iteration, effectively reducing the parallelism. This paper proposes a novel approach to reformulate the maximum likelihood expectation maximization (MLEM) algorithm so that it can scale up to many GPU nodes with less frequent inter-node communication. While being mathematically different, the new algorithm maximizes the same convex likelihood function as MLEM, thus converges to the same solution. Experiments on a multi-GPU cluster demonstrate the effectiveness of the proposed approach.

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.

GPU computing in medical physics: a review

The graphics processing unit (GPU) has emerged as a competitive platform for computing massively parallel problems. Many computing applications in medical physics can be formulated as data-parallel tasks that exploit the capabilities of the GPU for reducing processing times. The authors review the basic principles of GPU computing as well as the main performance optimization techniques, and survey existing applications in three areas of medical physics, namely image reconstruction, dose calculation and treatment plan optimization, and image processing.

Online detector response calculations for high-resolution PET image reconstruction

Positron emission tomography systems are best described by a linear shift-varying model. However, image reconstruction often assumes simplified shift-invariant models to the detriment of image quality and quantitative accuracy. We investigated a shift-varying model of the geometrical system response based on an analytical formulation. The model was incorporated within a list-mode, fully 3D iterative reconstruction process in which the system response coefficients are calculated online on a graphics processing unit (GPU). The implementation requires less than 512 Mb of GPU memory and can process two million events per minute (forward and backprojection). For small detector volume elements, the analytical model compared well to reference calculations. Images reconstructed with the shift-varying model achieved higher quality and quantitative accuracy than those that used a simpler shift-invariant model. For an 8 mm sphere in a warm background, the contrast recovery was 95.8% for the shift-varying model versus 85.9% for the shift-invariant model. In addition, the spatial resolution was more uniform across the field-of-view: for an array of 1.75 mm hot spheres in air, the variation in reconstructed sphere size was 0.5 mm RMS for the shift-invariant model, compared to 0.07 mm RMS for the shift-varying model.

GPU-accelerated 3D Bayesian image reconstruction from Compton scattered data

This paper describes the development of fast Bayesian reconstruction methods for Compton cameras using commodity graphics hardware. For fast iterative reconstruction, not only is it important to increase the convergence rate, but also it is equally important to accelerate the computation of time-consuming and repeated operations, such as projection and backprojection. Since the size of the system matrix for a typical Compton camera is intractably large, it is impractical to use a conventional caching scheme that stores the pre-calculated elements of a system matrix and uses them for the calculation of projection and backprojection. In this paper we propose GPU (graphics processing unit)-accelerated methods that can rapidly perform conical projection and backprojection on the fly. Since the conventional ray-based backprojection method is inefficient for parallel computing on GPUs, we develop voxel-based conical backprojection methods using two different approximation schemes. In the first scheme, we approximate the intersecting chord length of the ray passing through a voxel by the perpendicular distance from the center to the ray. In the second scheme, each voxel is regarded as a dimensionless point rather than a cube so that the backprojection can be performed without the need for calculating intersecting chord lengths or their approximations. Our simulation studies show that the GPU-based method dramatically improves the computational speed with only minor loss of accuracy in reconstruction. With the development of high-resolution detectors, the difference in the reconstruction accuracy between the GPU-based method and the CPU-based method will eventually be negligible.

Geometrical and Monte Carlo projectors in 3D PET reconstruction

PURPOSE

In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under consideration involves an extensive model of the system response matrix based on Monte Carlo simulations and is computed off-line and stored on disk.

METHODS

Comparisons were performed using simulated and experimental data of the commercial small animal PET scanner rPET.

RESULTS

The results demonstrate that the orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions yield better images in terms of contrast and spatial resolution than those obtained after using the conventional method and the multiray-based S-RT. Furthermore, the Monte Carlo-based method yields slight improvements in terms of contrast and spatial resolution with respect to these geometrical projectors.

CONCLUSIONS

The orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions represent satisfactory alternatives to factorizing the system matrix or to the conventional on-the-fly ray-tracing methods for list-mode reconstruction, where an extensive modeling based on Monte Carlo simulations is unfeasible.

Effects of multiple-interaction photon events in a high-resolution PET system that uses 3-D positioning detectors

PURPOSE

The authors' laboratory is developing a dual-panel, breast-dedicated PET system. The detector panels are built from dual-LSO-position-sensitive avalanche photodiode (PSAPD) modules-units holding two 8 x 8 arrays of 1 mm3 LSO crystals, where each array is coupled to a PSAPD. When stacked to form an imaging volume, these modules are capable of recording the 3-D coordinates of individual interactions of a multiple-interaction photon event (MIPE). The small size of the scintillation crystal elements used increases the likelihood of photon scattering between crystal arrays. In this article, the authors investigate how MIPEs impact the system photon sensitivity, the data acquisition scheme, and the quality and quantitative accuracy of reconstructed PET images.

METHODS

A Monte Carlo simulated PET scan using the dual-panel system was performed on a uniformly radioactive phantom for the photon sensitivity study. To establish the impact of MIPEs on a proposed PSAPD multiplexing scheme, experimental data were collected from a dual-LSO-PSAPD module edge-irradiated with a 22Na point source, the data were compared against simulation data based on an identical setup. To assess the impact of MIPEs on the dual-panel PET images, a simulated PET of a phantom comprising a matrix of hot spherical radiation sources of varying diameters immersed in a warm background was performed. The list-mode output data were used for image reconstruction, where various methods were used for estimating the location of the first photon interaction in MIPEs for more accurate line of response positioning. The contrast recovery coefficient (CRC), contrast to noise ratio (CNR), and the full width at half maximum spatial resolution of the spheres in the reconstructed images were used as figures of merit to facilitate comparison.

RESULTS

Compared to image reconstruction employing only events with interactions confined to one LSO array, a potential single photon sensitivity gain of > 46.9% (> 115.7% for coincidence) was noted for a uniform phantom when MIPEs with summed-energy falling within a +/- 12% window around the photopeak were also included. Both experimental and simulation data demonstrate that < 0.4% of the events whose summed-energy deposition falling within that energy window interacted with both crystal arrays within the same dual-LSO-PSAPD module. This result establishes the feasibility of a proposed multiplexed readout of analog output signals of the two PSAPDs within each module. Using MIPEs with summed-energy deposition within the 511 keV +/- 12% photopeak window and a new method for estimating the location of the first photon interaction in MIPEs, the corresponding reconstructed image exhibited a peak CNR of 7.23 for the 8 mm diameter phantom spheres versus a CNR of 6.69 from images based solely on single LSO array interaction events. The improved system photon sensitivity could be exploited to reduce the scan time by up to approximately 10%, while still maintaining image quality comparable to that achieved if MIPEs were excluded.

CONCLUSIONS

MIPE distribution in the detectors allows the proposed photodetector multiplexing arrangement without significant information loss. Furthermore, acquiring MIPEs can enhance system photon sensitivity and improve PET image CNR and CRC. The system under development can therefore competently acquire and analyze MIPEs and produce high-resolution PET images.

3D forward and back-projection for X-ray CT using separable footprints

Iterative methods for 3D image reconstruction have the potential to improve image quality over conventional filtered back projection (FBP) in X-ray computed tomography (CT). However, the computation burden of 3D cone-beam forward and back-projectors is one of the greatest challenges facing practical adoption of iterative methods for X-ray CT. Moreover, projector accuracy is also important for iterative methods. This paper describes two new separable footprint (SF) projector methods that approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. The SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction, whereas the SF-TT projector uses trapezoid functions in both directions. Simulations and experiments showed that both SF projector methods are more accurate than the distance-driven (DD) projector, which is a current state-of-the-art method in the field. The SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. The SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.