Fast EM-like methods for maximum "a posteriori" estimates in emission tomography

A comprehensive review on Compton camera image reconstruction: from principles to AI innovations

Compton cameras have emerged as promising tools in biomedical imaging, offering sensitive gamma-ray imaging capabilities for diverse applications. This review paper comprehensively overviews the latest advancements in Compton camera image reconstruction technologies. Beginning with a discussion of the fundamental principles of Compton scattering and its relevance to gamma-ray imaging, the paper explores the key components and design considerations of Compton camera systems. We then review various image reconstruction algorithms employed in Compton camera systems, including analytical, iterative, and statistical approaches. Recent developments in machine learning-based reconstruction methods are also discussed, highlighting their potential to enhance image quality and reduce reconstruction time in biomedical applications. In particular, we focus on the challenges posed by conical back-projection in Compton camera image reconstruction, and how innovative signal processing techniques have addressed these challenges to improve image accuracy and spatial resolution. Furthermore, experimental validations of Compton camera imaging in preclinical and clinical settings, including multi-tracer and whole-gamma imaging studies are introduced. In summary, this review provides potentially useful information about the current state-of-the-art Compton camera image reconstruction technologies, offering a helpful guide for investigators new to this field.

Deep learning-based PET image denoising and reconstruction: a review

This review focuses on positron emission tomography (PET) imaging algorithms and traces the evolution of PET image reconstruction methods. First, we provide an overview of conventional PET image reconstruction methods from filtered backprojection through to recent iterative PET image reconstruction algorithms, and then review deep learning methods for PET data up to the latest innovations within three main categories. The first category involves post-processing methods for PET image denoising. The second category comprises direct image reconstruction methods that learn mappings from sinograms to the reconstructed images in an end-to-end manner. The third category comprises iterative reconstruction methods that combine conventional iterative image reconstruction with neural-network enhancement. We discuss future perspectives on PET imaging and deep learning technology.

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.

Enhanced PET imaging using progressive conditional deep image prior

Objective.Unsupervised learning-based methods have been proven to be an effective way to improve the image quality of positron emission tomography (PET) images when a large dataset is not available. However, when the gap between the input image and the target PET image is large, direct unsupervised learning can be challenging and easily lead to reduced lesion detectability. We aim to develop a new unsupervised learning method to improve lesion detectability in patient studies.Approach.We applied the deep progressive learning strategy to bridge the gap between the input image and the target image. The one-step unsupervised learning is decomposed into two unsupervised learning steps. The input image of the first network is an anatomical image and the input image of the second network is a PET image with a low noise level. The output of the first network is also used as the prior image to generate the target image of the second network by iterative reconstruction method.Results.The performance of the proposed method was evaluated through the phantom and patient studies and compared with non-deep learning, supervised learning and unsupervised learning methods. The results showed that the proposed method was superior to non-deep learning and unsupervised methods, and was comparable to the supervised method.Significance.A progressive unsupervised learning method was proposed, which can improve image noise performance and lesion detectability.

An Investigation of Stochastic Variance Reduction Algorithms for Relative Difference Penalized 3D PET Image Reconstruction

Penalised PET image reconstruction algorithms are often accelerated during early iterations with the use of subsets. However, these methods may exhibit limit cycle behaviour at later iterations due to variations between subsets. Desirable converged images can be achieved for a subclass of these algorithms via the implementation of a relaxed step size sequence, but the heuristic selection of parameters will impact the quality of the image sequence and algorithm convergence rates. In this work, we demonstrate the adaption and application of a class of stochastic variance reduction gradient algorithms for PET image reconstruction using the relative difference penalty and numerically compare convergence performance to BSREM. The two investigated algorithms are: SAGA and SVRG. These algorithms require the retention in memory of recently computed subset gradients, which are utilised in subsequent updates. We present several numerical studies based on Monte Carlo simulated data and a patient data set for fully 3D PET acquisitions. The impact of the number of subsets, different preconditioners and step size methods on the convergence of regions of interest values within the reconstructed images is explored. We observe that when using constant preconditioning, SAGA and SVRG demonstrate reduced variations in voxel values between subsequent updates and are less reliant on step size hyper-parameter selection than BSREM reconstructions. Furthermore, SAGA and SVRG can converge significantly faster to the penalised maximum likelihood solution than BSREM, particularly in low count data.

Analysis of image quality by regulating beta function of BSREM reconstruction algorithm and comparison with conventional reconstructions in carcinoma breast studies of PET CT with BGO detector

BACKGROUND

The study aimed to evaluate the beta penalization factor of the BSREM reconstruction algorithm on a five-ring BGO-based PET CT system and compared it with conventional reconstructions.

METHODS

Retrospective study involves 30 breast cancer patient data of 18F-fluorodeoxyglucose ( 18 F-FDG) PET CT for reconstruction with OSEM, OSEM + PSF, and BSREM under variable β factors ranging from 200 to 600 in the steps of 50. Liver noise, lesion SUVmax, SBR, and SNR for each reconstruction were calculated. Quantitative parameters of each beta factor of BSREM were compared with OSEM and OSEM + PSF, using the Wilcoxon sign rank test with Bonferroni correction, a value of P < 0.002 was considered statistically significant. Visual scoring by two readers was also evaluated.

RESULTS

Thirty lesions of mean size 1.91 ± 0.58 cm range (0.7-3.6 cm) were identified. Liver noise and SBR were reduced, whereas SNR was increased with an increasing β value of BSREM. In comparison with OSEM, liver noise was not significantly different from β200 and β250. SNR of OSEM was significantly lower than any other β factors and SBR of β factor less than 500 was significantly higher than OSEM. In comparison with OSEM + PSF, liver noise was not significantly different from β400 and β350-500 do not show a significant difference in SNR and SBR compared with OSEM + PSF. β350 scored highest under visual scoring with a moderate agreement.

CONCLUSION

The study quantitatively indicates the optimum beta range of β250-450 and the qualitative evaluation indicates that β350 is an optimum beta factor of BSREM in breast cancer cases for 18 F-FDG WB-PET CT.

Positron Range Corrections and Denoising Techniques for Gallium-68 PET Imaging: A Literature Review

Gallium-68 (68Ga) is characterized by relatively high positron energy compared to Fluorine-18 (18F), causing substantial image quality degradation. Furthermore, the presence of statistical noise can further degrade image quality. The aim of this literature review is to identify the recently developed positron range correction techniques for 68Ga, as well as noise reduction methods to enhance the image quality of low count 68Ga PET imaging. The search engines PubMed and Scopus were employed, and we limited our research to published results from January 2010 until 1 August 2022. Positron range correction was achieved by using either deblurring or deep learning approaches. The proposed techniques improved the image quality and, in some cases, achieved an image quality comparable to 18F PET. However, none of these techniques was validated in clinical studies. PET denoising for 68Ga-labeled radiotracers was reported using either reconstruction-based techniques or deep learning approaches. It was demonstrated that both approaches can substantially enhance the image quality by reducing the noise levels of low count 68Ga PET imaging. The combination of 68Ga-specific positron range correction techniques and image denoising approaches may enable the application of low-count, high-quality 68Ga PET imaging in a clinical setting.

MR-guided motion-corrected PET image reconstruction for cardiac PET-MR

Simultaneous PET-MR imaging has shown potential for the comprehensive assessment of myocardial health from a single examination. Furthermore, MR-derived respiratory motion information has been shown to improve PET image quality by incorporating this information into the PET image reconstruction. Separately, MR-based anatomically guided PET image reconstruction has been shown to perform effective denoising, but this has been so far demonstrated mainly in brain imaging. To date the combined benefits of motion compensation and anatomical guidance have not been demonstrated for myocardial PET-MR imaging. This work addresses this by proposing a single cardiac PET-MR image reconstruction framework which fully utilises MR-derived information to allow both motion compensation and anatomical guidance within the reconstruction. Methods: Fifteen patients underwent a 18F-FDG cardiac PET-MR scan with a previously introduced acquisition framework. The MR data processing and image reconstruction pipeline produces respiratory motion fields and a high-resolution respiratory motion-corrected MR image with good tissue contrast. This MR-derived information was then included in a respiratory motion-corrected, cardiac-gated, anatomically guided image reconstruction of the simultaneously acquired PET data. Reconstructions were evaluated by measuring myocardial contrast and noise and compared to images from several comparative intermediate methods using the components of the proposed framework separately. Results: Including respiratory motion correction, cardiac gating, and anatomical guidance significantly increased contrast. In particular, myocardium-to-blood pool contrast increased by 143% on average (p<0.0001) compared to conventional uncorrected, non-guided PET images. Furthermore, anatomical guidance significantly reduced image noise compared to non-guided image reconstruction by 16.1% (p<0.0001). Conclusion: The proposed framework for MR-derived motion compensation and anatomical guidance of cardiac PET data was shown to significantly improve image quality compared to alternative reconstruction methods. Each component of the reconstruction pipeline was shown to have a positive impact on the final image quality. These improvements have the potential to improve clinical interpretability and diagnosis based on cardiac PET-MR images.

PET image reconstruction with deep progressive learning

Convolutional neural networks (CNNs) have recently achieved state-of-the-art results for positron emission tomography (PET) imaging problems. However direct learning from input image to target image is challenging if the gap is large between two images. Previous studies have shown that CNN can reduce image noise, but it can also degrade contrast recovery for small lesions. In this work, a deep progressive learning (DPL) method for PET image reconstruction is proposed to reduce background noise and improve image contrast. DPL bridges the gap between low quality image and high quality image through two learning steps. In the iterative reconstruction process, two pre-trained neural networks are introduced to control the image noise and contrast in turn. The feedback structure is adopted in the network design, which greatly reduces the parameters. The training data come from uEXPLORER, the world's first total-body PET scanner, in which the PET images show high contrast and very low image noise. We conducted extensive phantom and patient studies to test the algorithm for PET image quality improvement. The experimental results show that DPL is promising for reducing noise and improving contrast of PET images. Moreover, the proposed method has sufficient versatility to solve various imaging and image processing problems.

Post-reconstruction enhancement of [18F]FDG PET images with a convolutional neural network

BACKGROUND

The aim of the study was to develop and test an artificial intelligence (AI)-based method to improve the quality of [18F]fluorodeoxyglucose (FDG) positron emission tomography (PET) images.

METHODS

A convolutional neural network (CNN) was trained by using pairs of excellent (acquisition time of 6 min/bed position) and standard (acquisition time of 1.5 min/bed position) or sub-standard (acquisition time of 1 min/bed position) images from 72 patients. A test group of 25 patients was used to validate the CNN qualitatively and quantitatively with 5 different image sets per patient: 4 min/bed position, 1.5 min/bed position with and without CNN, and 1 min/bed position with and without CNN.

RESULTS

Difference in hotspot maximum or peak standardized uptake value between the standard 1.5 min and 1.5 min CNN images fell short of significance. Coefficient of variation, the noise level, was lower in the CNN-enhanced images compared with standard 1 min and 1.5 min images. Physicians ranked the 1.5 min CNN and the 4 min images highest regarding image quality (noise and contrast) and the standard 1 min images lowest.

CONCLUSIONS

AI can enhance [18F]FDG-PET images to reduce noise and increase contrast compared with standard images whilst keeping SUVmax/peak stability. There were significant differences in scoring between the 1.5 min and 1.5 min CNN image sets in all comparisons, the latter had higher scores in noise and contrast. Furthermore, difference in SUVmax and SUVpeak fell short of significance for that pair. The improved image quality can potentially be used either to provide better images to the nuclear medicine physicians or to reduce acquisition time/administered activity.

Does the beta regularization parameter of bayesian penalized likelihood reconstruction always affect the quantification accuracy and image quality of positron emission tomography computed tomography?

Purpose

This study aims to provide a detailed investigation on the noise penalization factor in Bayesian penalized likelihood (BPL)‐based algorithm, with the utilization of partial volume effect correction (PVC), so as to offer the suitable beta value and optimum standardized uptake value (SUV) parameters in clinical practice for small pulmonary nodules.

Methods

A National Electrical Manufacturers Association (NEMA) image‐quality phantom was scanned and images were reconstructed using BPL with beta values ranged from 100 to 1000. The recovery coefficient (RC), contrast recovery (CR), and background variability (BV) were measured to assess the quantification accuracy and image quality. In the clinical assessment, lesions were categorized into sub‐centimeter (<10 mm, n = 7) group and medium size (10–30 mm, n = 16) group. Signal‐to‐noise ratio (SNR) and contrast‐to‐noise ratio (CNR) were measured to evaluate the image quality and lesion detectability. With PVC was performed, the impact of beta values on SUVs (SUVmax, SUVmean, SUVpeak) of small pulmonary nodules was evaluated. Subjective image analysis was performed by two experienced readers.

Results

With the increasing of beta values, RC, CR, and BV decreased gradually in the phantom work. In the clinical study, SNR and CNR of both groups increased with the beta values (P < 0.001), although the sub‐centimeter group showed increases after the beta value reached over 700. In addition, highly significant negative correlations were observed between SUVs and beta values for both lesion‐size groups before the PVC (P < 0.001 for all). After the PVC, SUVpeak measured from the sub‐centimeter group was no significantly different among different beta values (P = 0.830).

Conclusion

Our study suggests using SUVpeak as the quantification parameter with PVC performed to mitigate the effects of beta regularization. Beta values between 300 and 400 were preferred for pulmonary nodules smaller than 30 mm.

OMEGA-open-source emission tomography software

In this paper we present OMEGA, an open-source software, for efficient and fast image reconstruction in positron emission tomography (PET). OMEGA uses the scripting language of MATLAB and GNU Octave allowing reconstruction of PET data with a MATLAB or GNU Octave interface. The goal of OMEGA is to allow easy and fast reconstruction of any PET data, and to provide a computationally efficient, easy-access platform for development of new PET algorithms with built-in forward and backward projection operations available to the user as a MATLAB/Octave class. OMEGA also includes direct support for GATE simulated data, facilitating easy evaluation of the new algorithms using Monte Carlo simulated PET data. OMEGA supports parallel computing by utilizing OpenMP for CPU implementations and OpenCL for GPU allowing any hardware to be used. OMEGA includes built-in function for the computation of normalization correction and allows several other corrections to be applied such as attenuation, randoms or scatter. OMEGA includes several different maximum-likelihood and maximum a posteriori (MAP) algorithms with several different priors. The user can also input their own priors to the built-in MAP functions. The image reconstruction in OMEGA can be computed either by using an explicitly computed system matrix or with a matrix-free formalism, where the latter can be accelerated with OpenCL. We provide an overview on the software and present some examples utilizing the different features of the software.

Image reconstruction methods affect software-aided assessment of pathologies of [18F]flutemetamol and [18F]FDG brain-PET examinations in patients with neurodegenerative diseases

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[¹⁸F]Flutemetamol and [¹⁸F]FDG image reconstruction.

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Software-aided assessment of neurodegenerative disease patients.

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New developments in brain PET image reconstruction affect quantitative measures.

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Evaluation of SUVR and z-score measures.

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Normalizing to pons and whole brain induced greater absolute differences between reconstructions.

Purpose

To assess how some of the new developments in brain positron emission tomography (PET) image reconstruction affect quantitative measures and software-aided assessment of pathology in patients with neurodegenerative diseases.

Methods

PET data were grouped into four cohorts: prodromal Alzheimer’s disease patients and controls receiving [¹⁸F]flutemetamol, and neurodegenerative disease patients and controls receiving [¹⁸F]FDG PET scans. Reconstructed images were obtained by ordered-subsets expectation maximization (OSEM; 3 iterations (i), 16/34 subsets (s), 3/5-mm filter, ±time-of-flight (TOF), ±point-spread function (PSF)) and block-sequential regularized expectation maximization (BSREM; TOF, PSF, β-value 75–300). Standardized uptake value ratios (SUVR) and z-scores were calculated (CortexID Suite, GE Healthcare) using cerebellar gray matter, pons, whole cerebellum and whole brain as reference regions.

Results

In controls, comparable results to the normal database were obtained with OSEM 3i/16 s 5-mm reconstruction. TOF, PSF and BSREM either increased or decreased the relative uptake difference to the normal subjects’ database within the software, depending on the tracer and chosen reference area, i.e. resulting in increased absolute z-scores. Normalizing to pons and whole brain for [¹⁸F]flutemetamol and [¹⁸F]FDG, respectively, increased absolute differences between reconstructions methods compared to normalizing to cerebellar gray matter and whole cerebellum when applying TOF, PSF and BSREM.

Conclusions

Software-aided assessment of patient pathologies should be used with caution when employing other image reconstruction methods than those used for acquisition of the normal database.

Evaluation of block-sequential regularized expectation maximization reconstruction of 68Ga-DOTATOC, 18F-fluoride, and 11C-acetate whole-body examinations acquired on a digital time-of-flight PET/CT scanner

Background

Block-sequential regularized expectation maximization (BSREM) is a fully convergent iterative image reconstruction algorithm. We hypothesize that tracers with different distribution patterns will result in different optimal settings for the BSREM algorithm. The aim of this study was to evaluate the image quality with variations in the applied β-value and acquisition time for three positron emission tomography (PET) tracers. NEMA image quality phantom measurements and clinical whole-body digital time-of-flight (TOF) PET/computed tomography (CT) examinations with ⁶⁸Ga-DOTATOC (n = 13), ¹⁸F-fluoride (n = 10), and ¹¹C-acetate (n = 13) were included. Each scan was reconstructed using BSREM with β-values of 133, 267, 400, and 533, and ordered subsets expectation maximization (OSEM; 3 iterations, 16 subsets, and 5-mm Gaussian post-processing filter). Both reconstruction methods included TOF and point spread function (PSF) recovery. Quantitative measures of noise, signal-to-noise ratio (SNR), and signal-to-background ratio (SBR) were analysed for various acquisition times per bed position (bp).

Results

The highest β-value resulted in the lowest level of noise, which in turn resulted in the highest SNR and lowest SBR. Noise levels equal to or lower than those of OSEM were found with β-values equal to or higher than 400, 533, and 267 for ⁶⁸Ga-DOTATOC, ¹⁸F-fluoride, and ¹¹C-acetate, respectively. The specified β-ranges resulted in increased SNR at a minimum of 25% (P < 0.0001) and SBR at a maximum of 23% (P < 0.0001) as compared to OSEM. At a reduced acquisition time by 25% for ⁶⁸Ga-DOTATOC and ¹⁸F-fluoride, and 67% for ¹¹C-acetate, BSREM with β-values equal to or higher than 533 resulted in noise equal to or lower than that of OSEM at full acquisition duration (2 min/bp for ⁶⁸Ga-DOTATOC and ¹⁸F-fluoride, 3 min/bp for ¹¹C-acetate). The reduced acquisition time with β 533 resulted in increased SNR (16–26%, P < 0.003) and SBR (6–18%, P < 0.0001 (P = 0.07 for ¹¹C-acetate)) compared to the full acquisition OSEM.

Conclusions

Within tracer-specific ranges of β-values, BSREM reconstruction resulted in increased SNR and SBR with respect to conventional OSEM reconstruction. Similar SNR, SBR, and noise levels could be attained with BSREM at relatively shorter acquisition times or, alternatively, lower administered dosages, compared to those attained with OSEM.

Optimization of [18F]PSMA-1007 PET-CT using regularized reconstruction in patients with prostate cancer

BACKGROUND

Prostate-specific membrane antigen (PSMA) radiotracers such as [¹⁸F]PSMA-1007 used with positron emission tomography-computed tomography (PET-CT) is promising for initial staging and detection of recurrent disease in prostate cancer patients. The block-sequential regularization expectation maximization algorithm (BSREM) is a new PET reconstruction algorithm, which provides higher image contrast while also reducing noise. The aim of the present study was to evaluate the influence of different acquisition times and different noise-suppressing factors in BSREM (β values) in [¹⁸F]PSMA-1007 PET-CT regarding quantitative data as well as a visual image quality assessment. We included 35 patients referred for clinical [¹⁸F]PSMA-1007 PET-CT. Four megabecquerels per kilogramme were administered and imaging was performed after 120 min. Eighty-four image series per patient were created with combinations of acquisition times of 1-4 min/bed position and β values of 300-1400. The noise level in normal tissue and the contrast-to-noise ratio (CNR) of pathological uptakes versus the local background were calculated. Image quality was assessed by experienced nuclear medicine physicians.

RESULTS

The noise level in the liver, spleen, and muscle was higher for low β values and low acquisition times (written as activity time products (ATs = administered activity × acquisition time)) and was minimized at maximum AT (16 MBq/kg min) and maximum β (1400). There was only a small decrease above AT 10. The median CNR increased slowly with AT from approximately 6 to 12 and was substantially lower at AT 4 and higher at AT 14-16. At AT 4-6, many images were regarded as being of unacceptable quality. For AT 8, β values of 700-900 were considered of acceptable quality.

CONCLUSIONS

An AT of 8 (for example as in our study, 4 MB/kg with an acquisition time of 2 min) with a β value of 700 performs well regarding noise level, CNR, and visual image quality assessment.

Faster PET reconstruction with non-smooth priors by randomization and preconditioning

Uncompressed clinical data from modern positron emission tomography (PET) scanners are very large, exceeding 350 million data points (projection bins). The last decades have seen tremendous advancements in mathematical imaging tools many of which lead to non-smooth (i.e. non-differentiable) optimization problems which are much harder to solve than smooth optimization problems. Most of these tools have not been translated to clinical PET data, as the state-of-the-art algorithms for non-smooth problems do not scale well to large data. In this work, inspired by big data machine learning applications, we use advanced randomized optimization algorithms to solve the PET reconstruction problem for a very large class of non-smooth priors which includes for example total variation, total generalized variation, directional total variation and various different physical constraints. The proposed algorithm randomly uses subsets of the data and only updates the variables associated with these. While this idea often leads to divergent algorithms, we show that the proposed algorithm does indeed converge for any proper subset selection. Numerically, we show on real PET data (FDG and florbetapir) from a Siemens Biograph mMR that about ten projections and backprojections are sufficient to solve the MAP optimisation problem related to many popular non-smooth priors; thus showing that the proposed algorithm is fast enough to bring these models into routine clinical practice.

Impact of acquisition time and penalizing factor in a block-sequential regularized expectation maximization reconstruction algorithm on a Si-photomultiplier-based PET-CT system for 18F-FDG

Background

Block-sequential regularized expectation maximization (BSREM), commercially Q. Clear (GE Healthcare, Milwaukee, WI, USA), is a reconstruction algorithm that allows for a fully convergent iterative reconstruction leading to higher image contrast compared to conventional reconstruction algorithms, while also limiting noise. The noise penalization factor β controls the trade-off between noise level and resolution and can be adjusted by the user. The aim was to evaluate the influence of different β values for different activity time products (ATs = administered activity × acquisition time) in whole-body ¹⁸F-fluorodeoxyglucose (FDG) positron emission tomography with computed tomography (PET-CT) regarding quantitative data, interpretation, and quality assessment of the images.

Twenty-five patients with known or suspected malignancies, referred for clinical ¹⁸F-FDG PET-CT examinations acquired on a silicon photomultiplier PET-CT scanner, were included. The data were reconstructed using BSREM with β values of 100–700 and ATs of 4–16 MBq/kg × min/bed (acquisition times of 1, 1.5, 2, 3, and 4 min/bed). Noise level, lesion SUV_max, and lesion SUV_peak were calculated. Image quality and lesion detectability were assessed by four nuclear medicine physicians for acquisition times of 1.0 and 1.5 min/bed position.

Results

The noise level decreased with increasing β values and ATs. Lesion SUV_max varied considerably between different β values and ATs, whereas SUV_peak was more stable. For an AT of 6 (in our case 1.5 min/bed), the best image quality was obtained with a β of 600 and the best lesion detectability with a β of 500. AT of 4 generated poor-quality images and false positive uptakes due to noise.

Conclusions

For oncologic whole-body ¹⁸F-FDG examinations on a SiPM-based PET-CT, we propose using an AT of 6 (i.e., 4 MBq/kg and 1.5 min/bed) reconstructed with BSREM using a β value of 500–600 in order to ensure image quality and lesion detection rate as well as a high patient throughput. We do not recommend using AT < 6 since the risk of false positive uptakes due to noise increases.

Regularized reconstruction of digital time-of-flight 68Ga-PSMA-11 PET/CT for the detection of recurrent disease in prostate cancer patients

Accurate localization of recurrent prostate cancer (PCa) is critical, especially if curative therapy is intended. With the aim to optimize target-to-background uptake ratio in ⁶⁸Ga-PSMA-11 PET, we investigated the image quality and quantitative measures of regularized reconstruction by block-sequential regularized expectation maximization (BSREM).

Methods: The study encompassed retrospective reconstruction and analysis of 20 digital time-of-flight (TOF) PET/CT examinations acquired 60 min post injection of 2 MBq/kg of ⁶⁸Ga-PSMA-11 in PCa patients with biochemical relapse after primary treatment. Reconstruction by ordered-subsets expectation maximization (OSEM; 3 iterations, 16 subsets, 5 mm gaussian postprocessing filter) and BSREM (β-values of 100-1600) were used, both including TOF and point spread function (PSF) recovery. Background variability (BV) was measured by placing a spherical volume of interest in the right liver lobe and defined as the standard deviation divided by the mean standardized uptake value (SUV). The image quality was evaluated in terms of signal-to-noise ratio (SNR) and signal-to-background ratio (SBR), using SUV_max of the lesions. A visual assessment was performed by four observers.

Results: OSEM reconstruction produced images with a BV of 15%, whereas BSREM with a β-value above 300 resulted in lower BVs than OSEM (36% with β 100, 8% with β 1300). Decreasing the acquisition duration from 2 to 1 and 0.5 min per bed position increased BV for both reconstruction methods, although BSREM with β-values equal to or higher than 800 and 1200, respectively, kept the BV below 15%. In comparison of BSREM with OSEM, the mean SNR improved by 25 to 66% with an increasing β-value in the range of 200-1300, whereas the mean SBR decreased with an increasing β-value, ranging from 0 to 125% with a β-value of 100 and 900, respectively. Decreased acquisition duration resulted in β-values of 800 to 1000 and 1200 to 1400 for 1 and 0.5 min per bed position, respectively, producing improved image quality measures compared with OSEM at a full acquisition duration of 2 min per bed position. The observer study showed a slight overall preference for BSREM β 900 although the interobserver variability was high.

Conclusion: BSREM image reconstruction with β-values in the range of 400-900 resulted in lower BV and similar or improved SNR and SBR in comparison with OSEM.

Impact of penalizing factor in a block-sequential regularized expectation maximization reconstruction algorithm for 18F-fluorocholine PET-CT regarding image quality and interpretation

BACKGROUND

Recently, the block-sequential regularized expectation maximization (BSREM) reconstruction algorithm was commercially introduced (Q.Clear, GE Healthcare, Milwaukee, WI, USA). However, the combination of noise-penalizing factor (β), acquisition time, and administered activity for optimal image quality has not been established for ¹⁸F-fluorocholine (FCH). The aim was to compare image quality and diagnostic performance of different reconstruction protocols for patients with prostate cancer being examined with ¹⁸F-FCH on a silicon photomultiplier-based PET-CT. Thirteen patients were included, injected with 4 MBq/kg, and images were acquired after 1 h. Images were reconstructed with frame durations of 1.0, 1.5, and 2.0 min using β of 150, 200, 300, 400, 500, and 550. An ordered subset expectation maximization (OSEM) reconstruction with a frame duration of 2.0 min was used for comparison. Images were quantitatively analyzed regarding standardized uptake values (SUV) in metastatic lymph nodes, local background, and muscle to obtain contrast-to-noise ratios (CNR) as well as the noise level in muscle. Images were analyzed regarding image quality and number of metastatic lymph nodes by two nuclear medicine physicians.

RESULTS

The highest median CNR was found for BSREM with a β of 300 and a frame duration of 2.0 min. The OSEM reconstruction had the lowest median CNR. Both the noise level and lesion SUV_max decreased with increasing β. For a frame duration of 1.5 min, the median quality score was highest for β 400-500, and for a frame duration of 2.0 min the score was highest for β 300-500. There was no statistically significant difference in the number of suspected lymph node metastases between the different image series for one of the physicians, and for the other physician the number of lymph nodes differed only for one combination of image series.

CONCLUSIONS

To achieve acceptable image quality at 4 MBq/kg ¹⁸F-FCH, we propose using a β of 400-550 with a frame duration of 1.5 min. The lower β should be used if a high CNR is desired and the higher if a low noise level is important.

Quantitative performance and optimal regularization parameter in block sequential regularized expectation maximization reconstructions in clinical 68Ga-PSMA PET/MR

BACKGROUND

In contrast to ordered subset expectation maximization (OSEM), block sequential regularized expectation maximization (BSREM) positron emission tomography (PET) reconstruction algorithms can run until full convergence while controlling image quality and noise. Recent studies with BSREM and 18F-FDG PET reported higher signal-to-noise ratios and higher standardized uptake values (SUV). In this study, we investigate the optimal regularization parameter (β) for clinical 68Ga-PSMA PET/MR reconstructions in the pelvic region applying time-of-flight (TOF) BSREM in comparison to TOF OSEM. Two-minute emission data from the pelvic region of 25 patients who underwent 68Ga-PSMA PET/MR were retrospectively reconstructed. Reference OSEM reconstructions had 28 subsets and 2 iterations. BSREM reconstructions were performed with 15 β values between 150 and 1200. Regions of interest (ROIs) were drawn around lesions and in uniform background. Background SUVmean (average) and SUVstd (standard deviation), and lesion SUVmax (average of 5 hottest voxels) were calculated. Differences were analyzed using the Wilcoxon matched pairs signed-rank test.

RESULTS

A total of 40 lesions were identified in the pelvic region. Background noise (SUVstd) and lesions SUVmax decreased with increasing β. Image reconstructions with β values lower than 400 have higher (p < 0.01) background noise, compared to the reference OSEM reconstructions, and are therefore less useful. Lesions with low activity on images reconstructed with β values higher than 600 have a lower (p < 0.05) SUVmax compared to the reference. These reconstructions are likely visually appealing due to the lower background noise, but the lower SUVmax could possibly render small low-uptake lesions invisible.

CONCLUSIONS

In our study, we showed that PET images reconstructed with TOF BSREM in combination with the 68Ga-PSMA tracer result in lower background noise and higher SUVmax values in lesions compared to TOF OSEM. Our study indicates that a β value between 400 and 550 might be the optimal compromise between high SUVmax and low background noise.

Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning

This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three ¹⁸F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.

Evaluation of Penalized-Likelihood Estimation Reconstruction on a Digital Time-of-Flight PET/CT Scanner for 18F-FDG Whole-Body Examinations

The resolution and quantitative accuracy of PET are highly influenced by the reconstruction method. Penalized-likelihood estimation algorithms allow for fully convergent iterative reconstruction, generating a higher image contrast than ordered-subsets expectation maximization (OSEM) while limiting noise. In this study, a type of penalized reconstruction known as block-sequential regularized expectation maximization (BSREM) was compared with time-of-flight OSEM (TOF OSEM). Various strengths of noise penalization factor β were tested along with various acquisition durations and transaxial fields of view (FOVs) with the aim of evaluating the performance and clinical use of BSREM for ¹⁸F-FDG PET/CT, both quantitatively and in a qualitative visual evaluation. Methods: Eleven clinical whole-body ¹⁸F-FDG PET/CT examinations acquired on a digital TOF PET/CT scanner were included. The data were reconstructed using BSREM with point-spread function recovery and β-factors of 133, 267, 400, and 533-and using TOF OSEM with point-spread function-for various acquisition times per bed position and various FOVs. Noise level, signal-to-noise ratio (SNR), signal-to-background ratio (SBR), and SUV were analyzed. A masked evaluation of visual image quality, rating several aspects, was performed by 2 nuclear medicine physicians to complement the analysis. Results: The lowest levels of noise were reached with the highest β-factor, resulting in the highest SNR, which in turn resulted in the lowest SBR. A β-factor of 400 gave noise equivalent to TOF OSEM but produced a significant increase in SUV_max (11%), SNR (22%), and SBR (12%). BSREM with a β-factor of 533 at a decreased acquisition duration (2 min/bed position) was comparable to TOF OSEM at a full acquisition duration (3 min/bed position). Reconstructed FOV had an impact on BSREM outcome measures; SNR increased and SBR decreased when FOV was shifted from 70 to 50 cm. The evaluation of visual image quality resulted in similar scores for reconstructions, although a β-factor of 400 obtained the highest mean whereas a β-factor of 267 was ranked best in overall image quality, contrast, sharpness, and tumor detectability. Conclusion: In comparison with TOF OSEM, penalized BSREM reconstruction resulted in an increased tumor SUV_max and an improved SNR and SBR at a matched level of noise. BSREM allowed for a shorter acquisition than TOF OSEM, with equal image quality.

Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction

Iterative methods for tomographic image reconstruction have the computational cost of each iteration dominated by the computation of the (back)projection operator, which take roughly O(N³) floating point operations (flops) for N × N pixels images. Furthermore, classical iterative algorithms may take too many iterations in order to achieve acceptable images, thereby making the use of these techniques unpractical for high-resolution images. Techniques have been developed in the literature in order to reduce the computational cost of the (back)projection operator to O(N²logN) flops. Also, incremental algorithms have been devised that reduce by an order of magnitude the number of iterations required to achieve acceptable images. The present paper introduces an incremental algorithm with a cost of O(N²logN) flops per iteration and applies it to the reconstruction of very large tomographic images obtained from synchrotron light illuminated data.

Joint estimation of activity image and attenuation sinogram using time-of-flight positron emission tomography data consistency condition filtering

Attenuation correction is essential for quantitative reliability of positron emission tomography (PET) imaging. In time-of-flight (TOF) PET, attenuation sinogram can be determined up to a global constant from noiseless emission data due to the TOF PET data consistency condition. This provides the theoretical basis for jointly estimating both activity image and attenuation sinogram/image directly from TOF PET emission data. Multiple joint estimation methods, such as maximum likelihood activity and attenuation (MLAA) and maximum likelihood attenuation correction factor (MLACF), have already been shown that can produce improved reconstruction results in TOF cases. However, due to the nonconcavity of the joint log-likelihood function and Poisson noise presented in PET data, the iterative method still requires proper initialization and well-designed regularization to prevent convergence to local maxima. To address this issue, we propose a joint estimation of activity image and attenuation sinogram using the TOF PET data consistency condition as an attenuation sinogram filter, and then evaluate the performance of the proposed method using computer simulations.

Clinical evaluation of a block sequential regularized expectation maximization reconstruction algorithm in 18F-FDG PET/CT studies

PURPOSE

To investigate the clinical performance of a block sequential regularized expectation maximization (BSREM) penalized likelihood reconstruction algorithm in oncologic PET/computed tomography (CT) studies.

METHODS

A total of 410 reconstructions of 41 fluorine-18 fluorodeoxyglucose-PET/CT studies of 41 patients with a total of 2010 lesions were analyzed by two experienced nuclear medicine physicians. Images were reconstructed with BSREM (with four different β values) or ordered subset expectation maximization (OSEM) algorithm with/without time-of-flight (TOF/non-TOF) corrections. OSEM reconstruction postfiltering was 4.0 mm full-width at half-maximum; BSREM did not use postfiltering. Evaluation of general image quality was performed with a five-point scale using maximum intensity projections. Artifacts (category 1), image sharpness (category 2), noise (category 3), and lesion detectability (category 4) were analyzed using a four-point scale. Size and maximum standardized uptake value (SUVmax) of lesions were measured by a third reader not involved in the image evaluation.

RESULTS

BSREM-TOF reconstructions showed the best results in all categories, independent of different body compartments. In all categories, BSREM non-TOF reconstructions were significantly better than OSEM non-TOF reconstructions (P<0.001). In almost all categories, BSREM non-TOF reconstruction was comparable to or better than the OSEM-TOF algorithm (P<0.001 for general image quality, image sharpness, noise, and P=1.0 for artifact). Only in lesion detectability was OSEM-TOF significantly better than BSREM non-TOF (P<0.001). Both BSREM-TOF and BSREM non-TOF showed a decreasing SUVmax with increasing β values (P<0.001) and TOF reconstructions showed a significantly higher SUVmax than non-TOF reconstructions (P<0.001).

CONCLUSION

The BSREM reconstruction algorithm showed a relevant improvement compared with OSEM reconstruction in PET/CT studies in all evaluated categories. BSREM might be used in clinical routine in conjunction with TOF to achieve better/higher image quality and lesion detectability or in PET/CT-systems without TOF-capability for enhancement of overall image quality as well.

New solid state cadmium-zinc-telluride technology for cardiac single photon emission computed tomographic myocardial perfusion imaging

INTRODUCTION

Single photon emission computed tomography (SPECT) myocardial perfusion imaging (MPI) is well established as diagnostic test for patients with suspected or known coronary artery disease. New camera systems have been developed with cadmium-zinc-telluride (CZT) detectors, novel collimator designs and reconstruction software. Areas covered: We review the current state of cardiac SPECT, advances in conventional camera technology and the development and clinical validation of solid-state CZT cameras. Expert commentary: The development of CZT systems is timely and addresses current issues for clinical SPECT imaging. These systems have a significant increase in photon sensitivity, permitting much lower radiation patient doses at a time when the lay and medical communities are very concerned about the radiation doses resulting from medical imaging. The increased count sensitivity permits shorter acquisition times and greater patient throughput which may address the ongoing and increasing issue of decreased funding for healthcare and, particularly, diagnostic imaging. The improved image resolution should improve diagnostic accuracy and increase the value of SPECT imaging for management of patients with CAD at a time of significant competition from other imaging modalities.

Evaluation of lesion detectability in positron emission tomography when using a convergent penalized likelihood image reconstruction method

We have previously developed a convergent penalized likelihood (PL) image reconstruction algorithm using the relative difference prior (RDP) and showed that it achieves more accurate lesion quantitation compared to ordered subsets expectation maximization (OSEM). We evaluated the detectability of low-contrast liver and lung lesions using the PL-RDP algorithm compared to OSEM. We performed a two-alternative forced choice study using a channelized Hotelling observer model that was previously validated against human observers. Lesion detectability showed a stronger dependence on lesion size for PL-RDP than OSEM. Lesion detectability was improved using time-of-flight (TOF) reconstruction, with greater benefit for the liver compared to the lung and with increasing benefit for decreasing lesion size and contrast. PL detectability was statistically significantly higher than OSEM for 20 mm liver lesions when contrast was [Formula: see text] ([Formula: see text]), and TOF PL detectability was statistically significantly higher than TOF OSEM for 15 and 20 mm liver lesions with contrast [Formula: see text] and [Formula: see text], respectively. For all other cases, there was no statistically significant difference between PL and OSEM ([Formula: see text]). For the range of studied lesion properties, lesion detectability using PL-RDP was equivalent or improved compared to using OSEM.

Reconstruction of coronary arteries from X-ray angiography: A review

Despite continuous progress in X-ray angiography systems, X-ray coronary angiography is fundamentally limited by its 2D representation of moving coronary arterial trees, which can negatively impact assessment of coronary artery disease and guidance of percutaneous coronary intervention. To provide clinicians with 3D/3D+time information of coronary arteries, methods computing reconstructions of coronary arteries from X-ray angiography are required. Because of several aspects (e.g. cardiac and respiratory motion, type of X-ray system), reconstruction from X-ray coronary angiography has led to vast amount of research and it still remains as a challenging and dynamic research area. In this paper, we review the state-of-the-art approaches on reconstruction of high-contrast coronary arteries from X-ray angiography. We mainly focus on the theoretical features in model-based (modelling) and tomographic reconstruction of coronary arteries, and discuss the evaluation strategies. We also discuss the potential role of reconstructions in clinical decision making and interventional guidance, and highlight areas for future research.

Sparse/Low Rank Constrained Reconstruction for Dynamic PET Imaging

In dynamic Positron Emission Tomography (PET), an estimate of the radio activity concentration is obtained from a series of frames of sinogram data taken at ranging in duration from 10 seconds to minutes under some criteria. So far, all the well-known reconstruction algorithms require known data statistical properties. It limits the speed of data acquisition, besides, it is unable to afford the separated information about the structure and the variation of shape and rate of metabolism which play a major role in improving the visualization of contrast for some requirement of the diagnosing in application. This paper presents a novel low rank-based activity map reconstruction scheme from emission sinograms of dynamic PET, termed as SLCR representing Sparse/Low Rank Constrained Reconstruction for Dynamic PET Imaging. In this method, the stationary background is formulated as a low rank component while variations between successive frames are abstracted to the sparse. The resulting nuclear norm and l₁ norm related minimization problem can also be efficiently solved by many recently developed numerical methods. In this paper, the linearized alternating direction method is applied. The effectiveness of the proposed scheme is illustrated on three data sets.

Quantitative comparison of OSEM and penalized likelihood image reconstruction using relative difference penalties for clinical PET

Ordered subset expectation maximization (OSEM) is the most widely used algorithm for clinical PET image reconstruction. OSEM is usually stopped early and post-filtered to control image noise and does not necessarily achieve optimal quantitation accuracy. As an alternative to OSEM, we have recently implemented a penalized likelihood (PL) image reconstruction algorithm for clinical PET using the relative difference penalty with the aim of improving quantitation accuracy without compromising visual image quality. Preliminary clinical studies have demonstrated visual image quality including lesion conspicuity in images reconstructed by the PL algorithm is better than or at least as good as that in OSEM images. In this paper we evaluate lesion quantitation accuracy of the PL algorithm with the relative difference penalty compared to OSEM by using various data sets including phantom data acquired with an anthropomorphic torso phantom, an extended oval phantom and the NEMA image quality phantom; clinical data; and hybrid clinical data generated by adding simulated lesion data to clinical data. We focus on mean standardized uptake values and compare them for PL and OSEM using both time-of-flight (TOF) and non-TOF data. The results demonstrate improvements of PL in lesion quantitation accuracy compared to OSEM with a particular improvement in cold background regions such as lungs.

Advances in software for faster procedure and lower radiotracer dose myocardial perfusion imaging

The American Society of Nuclear Cardiology has recently published documents that encourage laboratories to take all the appropriate steps to greatly decrease patient radiation dose and has set the goal of 50% of all myocardial perfusion studies performed with an associated radiation exposure of 9mSv by 2014. In the present work, a description of the major software techniques readily available to shorten procedure time and decrease injected activity is presented. Particularly new reconstruction methods and their ability to include means for resolution recovery and noise regularization are described. The use of these improved reconstruction algorithms results in a consistent reduction in acquisition time, injected activity and consequently in the radiation dose absorbed by the patient. The clinical implications to the use of these techniques are also described in terms of maintained and even improved study quality, accuracy and sensitivity for the detection of heart disease.

Acceleration of MAP-EM algorithm via over-relaxation

To improve the convergence rate of the effective maximum a posteriori expectation-maximization (MAP-EM) algorithm in tomographic reconstructions, this study proposes a modified MAP-EM which uses an over-relaxation factor to accelerate image reconstruction. The proposed method, called MAP-AEM, is evaluated and compared with the results for MAP-EM and for an ordered-subset algorithm, in terms of the convergence rate and noise properties. The results show that the proposed method converges numerically much faster than MAP-EM and with a speed that is comparable to that for an ordered-subset type method. The proposed method is effective in accelerating MAP-EM tomographic reconstruction.

3D reconstruction of scintillation light emission from proton pencil beams using limited viewing angles-a simulation study

An accurate and high-resolution quality assurance (QA) method for proton radiotherapy beams is necessary to ensure correct dose delivery to the target. Detectors based on a large volume of liquid scintillator have shown great promise in providing fast and high-resolution measurements of proton treatment fields. However, previous work with these detectors has been limited to two-dimensional measurements, and the quantitative measurement of dose distributions was lacking. The purpose of the current study is to assess the feasibility of reconstructing three-dimensional (3D) scintillation light distributions of spot scanning proton beams using a scintillation system. The proposed system consists of a tank of liquid scintillator imaged by charge-coupled device cameras at three orthogonal viewing angles. Because of the limited number of viewing angles, we developed a profile-based technique to obtain an initial estimate that can improve the quality of the 3D reconstruction. We found that our proposed scintillator system and profile-based technique can reconstruct a single energy proton beam in 3D with a gamma passing rate (3%/3 mm local) of 100.0%. For a single energy layer of an intensity modulated proton therapy prostate treatment plan, the proposed method can reconstruct the 3D light distribution with a gamma pass rate (3%/3 mm local) of 99.7%. In addition, we also found that the proposed method is effective in detecting errors in the treatment plan, indicating that it can be a very useful tool for 3D proton beam QA.

Quantitative statistical methods for image quality assessment

Quantitative measures of image quality and reliability are critical for both qualitative interpretation and quantitative analysis of medical images. While, in theory, it is possible to analyze reconstructed images by means of Monte Carlo simulations using a large number of noise realizations, the associated computational burden makes this approach impractical. Additionally, this approach is less meaningful in clinical scenarios, where multiple noise realizations are generally unavailable. The practical alternative is to compute closed-form analytical expressions for image quality measures. The objective of this paper is to review statistical analysis techniques that enable us to compute two key metrics: resolution (determined from the local impulse response) and covariance. The underlying methods include fixed-point approaches, which compute these metrics at a fixed point (the unique and stable solution) independent of the iterative algorithm employed, and iteration-based approaches, which yield results that are dependent on the algorithm, initialization, and number of iterations. We also explore extensions of some of these methods to a range of special contexts, including dynamic and motion-compensated image reconstruction. While most of the discussed techniques were developed for emission tomography, the general methods are extensible to other imaging modalities as well. In addition to enabling image characterization, these analysis techniques allow us to control and enhance imaging system performance. We review practical applications where performance improvement is achieved by applying these ideas to the contexts of both hardware (optimizing scanner design) and image reconstruction (designing regularization functions that produce uniform resolution or maximize task-specific figures of merit).

Incorporating anatomical side information into PET reconstruction using nonlocal regularization

With the introduction of combined positron emission tomography (PET)/computed tomography (CT) or PET/magnetic resonance imaging (MRI) scanners, there is an increasing emphasis on reconstructing PET images with the aid of the anatomical side information obtained from X-ray CT or MRI scanners. In this paper, we propose a new approach to incorporating prior anatomical information into PET reconstruction using the nonlocal regularization method. The nonlocal regularizer developed for this application is designed to selectively consider the anatomical information only when it is reliable. As our proposed nonlocal regularization method does not directly use anatomical edges or boundaries which are often used in conventional methods, it is not only free from additional processes to extract anatomical boundaries or segmented regions, but also more robust to the signal mismatch problem that is caused by the indirect relationship between the PET image and the anatomical image. We perform simulations with digital phantoms. According to our experimental results, compared to the conventional method based on the traditional local regularization method, our nonlocal regularization method performs well even with the imperfect prior anatomical information or in the presence of signal mismatch between the PET image and the anatomical image.

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.

Regularized image reconstruction algorithms for dual-isotope myocardial perfusion SPECT (MPS) imaging using a cross-tracer prior

In simultaneous dual-isotope myocardial perfusion SPECT (MPS) imaging, data are simultaneously acquired to determine the distributions of two radioactive isotopes. The goal of this work was to develop penalized maximum likelihood (PML) algorithms for a novel cross-tracer prior that exploits the fact that the two images reconstructed from simultaneous dual-isotope MPS projection data are perfectly registered in space. We first formulated the simultaneous dual-isotope MPS reconstruction problem as a joint estimation problem. A cross-tracer prior that couples voxel values on both images was then proposed. We developed an iterative algorithm to reconstruct the MPS images that converges to the maximum a posteriori solution for this prior based on separable surrogate functions. To accelerate the convergence, we developed a fast algorithm for the cross-tracer prior based on the complete data OS-EM (COSEM) framework. The proposed algorithm was compared qualitatively and quantitatively to a single-tracer version of the prior that did not include the cross-tracer term. Quantitative evaluations included comparisons of mean and standard deviation images as well as assessment of image fidelity using the mean square error. We also evaluated the cross tracer prior using a three-class observer study with respect to the three-class MPS diagnostic task, i.e., classifying patients as having either no defect, reversible defect, or fixed defects. For this study, a comparison with conventional ordered subsets-expectation maximization (OS-EM) reconstruction with postfiltering was performed. The comparisons to the single-tracer prior demonstrated similar resolution for areas of the image with large intensity changes and reduced noise in uniform regions. The cross-tracer prior was also superior to the single-tracer version in terms of restoring image fidelity. Results of the three-class observer study showed that the proposed cross-tracer prior and the convergent algorithms improved the image quality of dual-isotope MPS images compared to OS-EM.

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.

Image reconstruction for PET/CT scanners: past achievements and future challenges

PET is a medical imaging modality with proven clinical value for disease diagnosis and treatment monitoring. The integration of PET and CT on modern scanners provides a synergy of the two imaging modalities. Through different mathematical algorithms, PET data can be reconstructed into the spatial distribution of the injected radiotracer. With dynamic imaging, kinetic parameters of specific biological processes can also be determined. Numerous efforts have been devoted to the development of PET image reconstruction methods over the last four decades, encompassing analytic and iterative reconstruction methods. This article provides an overview of the commonly used methods. Current challenges in PET image reconstruction include more accurate quantitation, TOF imaging, system modeling, motion correction and dynamic reconstruction. Advances in these aspects could enhance the use of PET/CT imaging in patient care and in clinical research studies of pathophysiology and therapeutic interventions.

Regularized Fully 5D Reconstruction of Cardiac Gated Dynamic SPECT Images

In our recent work, we proposed an image reconstruction procedure aimed to unify gated imaging and dynamic imaging in nuclear cardiac imaging. With this procedure the goal is to obtain an image sequence from a single acquisition which shows simultaneously both cardiac motion and tracer distribution change over the course of imaging. In this work, we further develop and demonstrate this procedure for fully 5D (3D space plus time plus gate) reconstruction in gated, dynamic cardiac SPECT imaging, where the challenge is even greater without the use of multiple fast camera rotations. For 5D reconstruction, we develop and compare two iterative algorithms: one is based on the modified block sequential regularized EM (BSREM-II) algorithm, and the other is based on the one-step late (OSL) algorithm. In our experiments, we simulated gated cardiac imaging with the NURBS-based cardiac-torso (NCAT) phantom and Tc99m-Teboroxime as the imaging agent, where acquisition with the equivalent of only three full camera rotations was used during the course of a 12-minute postinjection period. We conducted a thorough evaluation of the reconstruction results using a number of quantitative measures. Our results demonstrate that the 5D reconstruction procedure can yield gated dynamic images which show quantitative information for both perfusion defect detection and cardiac motion.

Iterative PET Image Reconstruction Using Translation Invariant Wavelet Transform

The present work describes a Bayesian maximum a posteriori (MAP) method using a statistical multiscale wavelet prior model. Rather than using the orthogonal discrete wavelet transform (DWT), this prior is built on the translation invariant wavelet transform (TIWT). The statistical modeling of wavelet coefficients relies on the generalized Gaussian distribution. Image reconstruction is performed in spatial domain with a fast block sequential iteration algorithm. We study theoretically the TIWT MAP method by analyzing the Hessian of the prior function to provide some insights on noise and resolution properties of image reconstruction. We adapt the key concept of local shift invariance and explore how the TIWT MAP algorithm behaves with different scales. It is also shown that larger support wavelet filters do not offer better performance in contrast recovery studies. These theoretical developments are confirmed through simulation studies. The results show that the proposed method is more attractive than other MAP methods using either the conventional Gibbs prior or the DWT-based wavelet prior.

Motion-compensated iterative cone-beam CT image reconstruction with adapted blobs as basis functions

This paper presents a three-dimensional method to reconstruct moving objects from cone-beam X-ray projections using an iterative reconstruction algorithm and a given motion vector field. For the image representation, adapted blobs are used, which can be implemented efficiently as basis functions. Iterative reconstruction requires the calculation of line integrals (forward projections) through the image volume, which are compared with the actual measurements to update the image volume. In the existence of a divergent motion vector field, a change in the volumes of the blobs has to be taken into account in the forward and backprojections. An efficient method to calculate the line integral through the adapted blobs is proposed. It solves the problem, how to compensate for the divergence in the motion vector field on a grid of basis functions. The method is evaluated on two phantoms, which are subject to three different known motions. Moreover, a motion-compensated filtered back-projection reconstruction method is used, and the reconstructed images are compared. Using the correct motion vector field with the iterative motion-compensated reconstruction, sharp images are obtained, with a quality that is significantly better than gated reconstructions.