A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography

Joint estimation of activity, attenuation and motion in respiratory-self-gated time-of-flight PET

Objective. Whole-body positron emission tomography (PET) imaging is often hindered by respiratory motion during acquisition, causing significant degradation in the quality of reconstructed activity images. An additional challenge in PET/CT imaging arises from the respiratory phase mismatch between CT-based attenuation correction and PET acquisition, leading to attenuation artifacts. To address these issues, we propose two new, purely data-driven methods for the joint estimation of activity, attenuation, and motion in respiratory self-gated time-of-flight PET. These methods enable the reconstruction of a single activity image free from motion and attenuation artifacts.Approach. The proposed methods were evaluated using data from the anthropomorphic Wilhelm phantom acquired on a Siemens mCT PET/CT system, as well as three clinical [18F]FDG PET/CT datasets acquired on a GE DMI PET/CT system. Image quality was assessed visually to identify motion and attenuation artifacts. Lesion uptake values were quantitatively compared across reconstructions without motion modeling, with motion modeling but 'static' attenuation correction, and with our proposed methods.Main results. For the Wilhelm phantom, the proposed methods delivered image quality closely matching the reference reconstruction from a static acquisition. The lesion-to-background contrast for a liver dome lesion improved from 2.0 (no motion correction) to 5.2 (using our proposed methods), matching the contrast from the static acquisition (5.2). In contrast, motion modeling with 'static' attenuation correction yielded a lower contrast of 3.5. In patient datasets, the proposed methods successfully reduced motion artifacts in lung and liver lesions and mitigated attenuation artifacts, demonstrating superior lesion to background separation.Significance. Our proposed methods enable the reconstruction of a single, high-quality activity image that is motion-corrected and free from attenuation artifacts, without the need for external hardware.

Bimodal PET/MRI generative reconstruction based on VAE architectures

Objective.In this study, we explore positron emission tomography (PET)/magnetic resonance imaging (MRI) joint reconstruction within a deep learning framework, introducing a novel synergistic method.Approach.We propose a new approach based on a variational autoencoder (VAE) constraint combined with the alternating direction method of multipliers (ADMM) optimization technique. We explore three VAE architectures, joint VAE, product of experts-VAE and multimodal JS divergence (MMJSD), to determine the optimal latent representation for the two modalities. We then trained and evaluated the architectures on a brain PET/MRI dataset.Main results.We showed that our approach takes advantage of each modality sharing information to each other, which results in improved peak signal-to-noise ratio and structural similarity as compared with traditional reconstruction, particularly for short acquisition times. We find that the one particular architecture, MMJSD, is the most effective for our methodology.Significance.The proposed method outperforms conventional approaches especially in noisy and undersampled conditions by making use of the two modalities together to compensate for the missing information.

PET image reconstruction using weighted nuclear norm maximization and deep learning prior

The ill-posed Positron emission tomography (PET) reconstruction problem usually results in limited resolution and significant noise. Recently, deep neural networks have been incorporated into PET iterative reconstruction framework to improve the image quality. In this paper, we propose a new neural network-based iterative reconstruction method by using weighted nuclear norm (WNN) maximization, which aims to recover the image details in the reconstruction process. The novelty of our method is the application of WNN maximization rather than WNN minimization in PET image reconstruction. Meanwhile, a neural network is used to control the noise originated from WNN maximization. Our method is evaluated on simulated and clinical datasets. The simulation results show that the proposed approach outperforms state-of-the-art neural network-based iterative methods by achieving the best contrast/noise tradeoff with a remarkable contrast improvement on the lesion contrast recovery. The study on clinical datasets also demonstrates that our method can recover lesions of different sizes while suppressing noise in various low-dose PET image reconstruction tasks. Our code is available athttps://github.com/Kuangxd/PETReconstruction.

ReconU-Net: a direct PET image reconstruction using U-Net architecture with back projection-induced skip connection

Objective.This study aims to introduce a novel back projection-induced U-Net-shaped architecture, called ReconU-Net, based on the original U-Net architecture for deep learning-based direct positron emission tomography (PET) image reconstruction. Additionally, our objective is to visualize the behavior of direct PET image reconstruction by comparing the proposed ReconU-Net architecture with the original U-Net architecture and existing DeepPET encoder-decoder architecture without skip connections.Approach. The proposed ReconU-Net architecture uniquely integrates the physical model of the back projection operation into the skip connection. This distinctive feature facilitates the effective transfer of intrinsic spatial information from the input sinogram to the reconstructed image via an embedded physical model. The proposed ReconU-Net was trained using Monte Carlo simulation data from the Brainweb phantom and tested on both simulated and real Hoffman brain phantom data.Main results. The proposed ReconU-Net method provided better reconstructed image in terms of the peak signal-to-noise ratio and contrast recovery coefficient than the original U-Net and DeepPET methods. Further analysis shows that the proposed ReconU-Net architecture has the ability to transfer features of multiple resolutions, especially non-abstract high-resolution information, through skip connections. Unlike the U-Net and DeepPET methods, the proposed ReconU-Net successfully reconstructed the real Hoffman brain phantom, despite limited training on simulated data.Significance. The proposed ReconU-Net can improve the fidelity of direct PET image reconstruction, even with small training datasets, by leveraging the synergistic relationship between data-driven modeling and the physics model of the imaging process.

A Review on Low-Dose Emission Tomography Post-Reconstruction Denoising with Neural Network Approaches

Low-dose emission tomography (ET) plays a crucial role in medical imaging, enabling the acquisition of functional information for various biological processes while minimizing the patient dose. However, the inherent randomness in the photon counting process is a source of noise which is amplified low-dose ET. This review article provides an overview of existing post-processing techniques, with an emphasis on deep neural network (NN) approaches. Furthermore, we explore future directions in the field of NN-based low-dose ET. This comprehensive examination sheds light on the potential of deep learning in enhancing the quality and resolution of low-dose ET images, ultimately advancing the field of medical imaging.

Super Resolution Dual-Energy Cone-Beam CT Imaging With Dual-Layer Flat-Panel Detector

In flat-panel detector (FPD) based cone-beam computed tomography (CBCT) imaging, the native receptor array is usually binned into a smaller matrix size. By doing so, the signal readout speed could be increased by 4-9 times at the expense of a spatial resolution loss of 50%-67%. Clearly, such manipulation poses a key bottleneck in generating high spatial and high temporal resolution CBCT images at the same time. In addition, the conventional FPD is also difficult in generating dual-energy CBCT images. In this paper, we propose an innovative super resolution dual-energy CBCT imaging method, named as suRi, based on dual-layer FPD (DL-FPD) to overcome these aforementioned difficulties at once. With suRi, specifically, a 1D or 2D sub-pixel (half pixel in this study) shifted binning is applied instead of the conventionally aligned binning to double the spatial sampling rate during the dual-energy data acquisition. As a result, the suRi approach provides a new strategy to enable high spatial resolution CBCT imaging while at high readout speed. Moreover, a penalized likelihood material decomposition algorithm is developed to directly reconstruct the high resolution bases from these dual-energy CBCT projections containing sub-pixel shifts. Numerical and physical experiments are performed to validate this newly developed suRi method with phantoms and biological specimen. Results demonstrate that suRi can significantly improve the spatial resolution of the CBCT image. We believe this developed suRi method would greatly enhance the imaging performance of the DL-FPD based dual-energy CBCT systems in future.

Evaluation of Non-Invasive Methods for (R)-[11C]PK11195 PET Image Quantification in Multiple Sclerosis

This study aims to evaluate non-invasive PET quantification methods for (R)-[11C]PK11195 uptake measurement in multiple sclerosis (MS) patients and healthy controls (HC) in comparison with arterial input function (AIF) using dynamic (R)-[11C]PK11195 PET and magnetic resonance images. The total volume of distribution (VT) and distribution volume ratio (DVR) were measured in the gray matter, white matter, caudate nucleus, putamen, pallidum, thalamus, cerebellum, and brainstem using AIF, the image-derived input function (IDIF) from the carotid arteries, and pseudo-reference regions from supervised clustering analysis (SVCA). Uptake differences between MS and HC groups were tested using statistical tests adjusted for age and sex, and correlations between the results from the different quantification methods were also analyzed. Significant DVR differences were observed in the gray matter, white matter, putamen, pallidum, thalamus, and brainstem of MS patients when compared to the HC group. Also, strong correlations were found in DVR values between non-invasive methods and AIF (0.928 for IDIF and 0.975 for SVCA, p < 0.0001). On the other hand, (R)-[11C]PK11195 uptake could not be differentiated between MS patients and HC using VT values, and a weak correlation (0.356, p < 0.0001) was found between VTAIF and VTIDIF. Our study shows that the best alternative for AIF is using SVCA for reference region modeling, in addition to a cautious and appropriate methodology.

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.

AI for PET image reconstruction

Image reconstruction for positron emission tomography (PET) has been developed over many decades, with advances coming from improved modelling of the data statistics and improved modelling of the imaging physics. However, high noise and limited spatial resolution have remained issues in PET imaging, and state-of-the-art PET reconstruction has started to exploit other medical imaging modalities (such as MRI) to assist in noise reduction and enhancement of PET's spatial resolution. Nonetheless, there is an ongoing drive towards not only improving image quality, but also reducing the injected radiation dose and reducing scanning times. While the arrival of new PET scanners (such as total body PET) is helping, there is always a need to improve reconstructed image quality due to the time and count limited imaging conditions. Artificial intelligence (AI) methods are now at the frontier of research for PET image reconstruction. While AI can learn the imaging physics as well as the noise in the data (when given sufficient examples), one of the most common uses of AI arises from exploiting databases of high-quality reference examples, to provide advanced noise compensation and resolution recovery. There are three main AI reconstruction approaches: (i) direct data-driven AI methods which rely on supervised learning from reference data, (ii) iterative (unrolled) methods which combine our physics and statistical models with AI learning from data, and (iii) methods which exploit AI with our known models, but crucially can offer benefits even in the absence of any example training data whatsoever. This article reviews these methods, considering opportunities and challenges of AI for PET reconstruction.

SPECT reconstruction with a trained regularizer using CT-side information: Application to 177Lu SPECT imaging

Improving low-count SPECT can shorten scans and support pre-therapy theranostic imaging for dosimetry-based treatment planning, especially with radionuclides like 177Lu known for low photon yields. Conventional methods often underperform in low-count settings, highlighting the need for trained regularization in model-based image reconstruction. This paper introduces a trained regularizer for SPECT reconstruction that leverages segmentation based on CT imaging. The regularizer incorporates CT-side information via a segmentation mask from a pre-trained network (nnUNet). In this proof-of-concept study, we used patient studies with 177Lu DOTATATE to train and tested with phantom and patient datasets, simulating pre-therapy imaging conditions. Our results show that the proposed method outperforms both standard unregularized EM algorithms and conventional regularization with CT-side information. Specifically, our method achieved marked improvements in activity quantification, noise reduction, and root mean square error. The enhanced low-count SPECT approach has promising implications for theranostic imaging, post-therapy imaging, whole body SPECT, and reducing SPECT acquisition times.

Performance study of a 360° CZT camera for monitoring 177Lu-PSMA treatment

BACKGROUND

The aim of this study was to investigate the quantification performance of a 360° CZT camera for 177Lu-based treatment monitoring.

METHODS

Three phantoms with known 177Lu activity concentrations were acquired: (1) a uniform cylindrical phantom for calibration, (2) a NEMA IEC body phantom for analysis of different-sized spheres to optimise quantification parameters and (3) a phantom containing two large vials simulating organs at risk for tests. Four sets of reconstruction parameters were tested: (1) Scatter, (2) Scatter and Point Spread Function Recovery (PSFR), (3) PSFR only and (4) Penalised likelihood option and Scatter, varying the number of updates (iterations × subsets) with CT-based attenuation correction only. For each, activity concentration (ARC) and contrast recovery coefficients (CRC) were estimated as well as root mean square. Visualisation and quantification parameters were applied to reconstructed patient image data.

RESULTS

Optimised quantification parameters were determined to be: CT-based attenuation correction, scatter correction, 12 iterations, 8 subsets and no filter. ARC, CRC and RMS results were dependant on the methodology used for calculations. Two different reconstruction parameters were recommended for visualisation and for quantification. 3D whole-body SPECT images were acquired and reconstructed for 177Lu-PSMA patients in 2-3 times faster than the time taken for a conventional gamma camera.

CONCLUSION

Quantification of whole-body 3D images of patients treated with 177Lu-PSMA is feasible and an optimised set of parameters has been determined. This camera greatly reduces procedure time for whole-body SPECT.

Comparison of post reconstruction- and reconstruction-based deep learning denoising methods in cardiac SPECT

Objective. The quality of myocardial perfusion SPECT (MPS) images is often hampered by low count statistics. Poor image quality might hinder reporting the studies and in the worst case lead to erroneous diagnosis. Deep learning (DL)-based methods can be used to improve the quality of the low count studies. DL can be applied in several different methods, which might affect the outcome. The aim of this study was to investigate the differences between post reconstruction- and reconstruction-based denoising methods.Approach. A UNET-type network was trained using ordered subsets expectation maximization (OSEM) reconstructed MPS studies acquired with half, quarter and eighth of full-activity. The trained network was applied as a post reconstruction denoiser (OSEM+DL) and it was incorporated into a regularized reconstruction algorithm as a deep learning penalty (DLP). OSEM+DL and DLP were compared against each other and against OSEM images without DL denoising in terms of noise level, myocardium-ventricle contrast and defect detection performance with signal-to-noise ratio of a non-prewhitening matched filter (NPWMF-SNR) applied to artificial perfusion defects inserted into defect-free clinical MPS scans. Comparisons were made using half-, quarter- and eighth-activity data.Main results. OSEM+DL provided lower noise level at all activities than other methods. DLP's noise level was also always lower than matching activity OSEM's. In addition, OSEM+DL and DLP outperformed OSEM in defect detection performance, but contrary to noise level ranking DLP had higher NPWMF-SNR overall than OSEM+DL. The myocardium-ventricle contrast was highest with DLP and lowest with OSEM+DL. Both OSEM+DL and DLP offered better image quality than OSEM, but visually perfusion defects were deeper in OSEM images at low activities.Significance. Both post reconstruction- and reconstruction-based DL denoising methods have great potential for MPS. The preference between these methods is a trade-off between smoother images and better defect detection performance.

Similarity-Driven Fine-Tuning Methods for Regularization Parameter Optimization in PET Image Reconstruction

We present an adaptive method for fine-tuning hyperparameters in edge-preserving regularization for PET image reconstruction. For edge-preserving regularization, in addition to the smoothing parameter that balances data fidelity and regularization, one or more control parameters are typically incorporated to adjust the sensitivity of edge preservation by modifying the shape of the penalty function. Although there have been efforts to develop automated methods for tuning the hyperparameters in regularized PET reconstruction, the majority of these methods primarily focus on the smoothing parameter. However, it is challenging to obtain high-quality images without appropriately selecting the control parameters that adjust the edge preservation sensitivity. In this work, we propose a method to precisely tune the hyperparameters, which are initially set with a fixed value for the entire image, either manually or using an automated approach. Our core strategy involves adaptively adjusting the control parameter at each pixel, taking into account the degree of patch similarities calculated from the previous iteration within the pixel's neighborhood that is being updated. This approach allows our new method to integrate with a wide range of existing parameter-tuning techniques for edge-preserving regularization. Experimental results demonstrate that our proposed method effectively enhances the overall reconstruction accuracy across multiple image quality metrics, including peak signal-to-noise ratio, structural similarity, visual information fidelity, mean absolute error, root-mean-square error, and mean percentage error.

Probabilistic deconvolution of PET images using informed priors

Purpose

We present a probabilistic approach to medical image analysis that requires, and makes use of, explicit prior information provided by a medical expert. Depending on the choice of prior model the method can be used for image enhancement, analysis, and segmentation.

Methods

The methodology is based on a probabilistic approach to medical image analysis, that allows integration of 1) arbitrarily complex prior information (for which realizations can be generated), 2) information about a convolution operator of the imaging system, and 3) information about the noise in the reconstructed image into a posterior probability density. The method was demonstrated on positron emission tomography (PET) images obtained from a phantom and a patient with lung cancer. The likelihood model (multivariate log-normal) and the convolution operator were derived from phantom data. Two examples of prior information were used to show the potential of the method. The extended Metropolis-Hastings algorithm, a Markov chain Monte Carlo method, was used to generate realizations of the posterior distribution of the tracer activity concentration.

Results

A set of realizations from the posterior was used as the base of a quantitative PET image analysis. The mean and variance of activity concentrations were computed, as well as the probability of high tracer uptake and statistics on the size and activity concentration of high uptake regions. For both phantom and in vivo images, the estimated images of mean activity concentrations appeared to have reduced noise levels, and a sharper outline of high activity regions, as compared to the original PET. The estimated variance of activity concentrations was high at the edges of high activity regions.

Conclusions

The methodology provides a probabilistic approach for medical image analysis that explicitly takes into account medical expert knowledge as prior information. The presented first results indicate the potential of the method to improve the detection of small lesions. The methodology allows for a probabilistic measure of the size and activity level of high uptake regions, with possible long-term perspectives for early detection of cancer, as well as treatment, planning, and follow-up.

Model-based three-material decomposition in dual-energy CT using the volume conservation constraint

Objective. We develop a model-based optimization algorithm for 'one-step' dual-energy (DE) CT decomposition of three materials directly from projection measurements.Approach.Since the three-material problem is inherently undetermined, we incorporate the volume conservation principle (VCP) as a pair of equality and nonnegativity constraints into the objective function of the recently reported model-based material decomposition (MBMD). An optimization algorithm (constrained MBMD, CMBMD) is derived that utilizes voxel-wise separability to partition the volume into a VCP-constrained region solved using interior-point iterations, and an unconstrained region (air surrounding the object, where VCP is violated) solved with conventional two-material MBMD. Constrained MBMD (CMBMD) is validated in simulations and experiments in application to bone composition measurements in the presence of metal hardware using DE cone-beam CT (CBCT). A kV-switching protocol with non-coinciding low- and high-energy (LE and HE) projections was assumed. CMBMD with decomposed base materials of cortical bone, fat, and metal (titanium, Ti) is compared to MBMD with (i) fat-bone and (ii) fat-Ti bases.Main results.Three-material CMBMD exhibits a substantial reduction in metal artifacts relative to the two-material MBMD implementations. The accuracies of cortical bone volume fraction estimates are markedly improved using CMBMD, with ∼5-10× lower normalized root mean squared error in simulations with anthropomorphic knee phantoms (depending on the complexity of the metal component) and ∼2-2.5× lower in an experimental test-bench study.Significance.In conclusion, we demonstrated one-step three-material decomposition of DE CT using volume conservation as an optimization constraint. The proposed method might be applicable to DE applications such as bone marrow edema imaging (fat-bone-water decomposition) or multi-contrast imaging, especially on CT/CBCT systems that do not provide coinciding LE and HE ray paths required for conventional projection-domain DE decomposition.

Performing tomographic reconstructions from a satellite looking toward Earth. Part 2: analysis of image quality

This paper is part 2 of two papers that explore performing tomographic reconstructions from a space platform. A simplified model of short-wave infrared emissions in the atmosphere is given. Simulations were performed that tested the effectiveness of reconstructions given signal amplitude, frequency, signal-to-noise ratio, number of iterations run, and others. Maximum likelihood expectation maximization is shown to be effective for reconstructing low signal cases.

Multi-channel convolutional analysis operator learning for dual-energy CT reconstruction

Objective. Dual-energy computed tomography (DECT) has the potential to improve contrast and reduce artifacts and the ability to perform material decomposition in advanced imaging applications. The increased number of measurements results in a higher radiation dose, and it is therefore essential to reduce either the number of projections for each energy or the source x-ray intensity, but this makes tomographic reconstruction more ill-posed. Approach. We developed the multi-channel convolutional analysis operator learning (MCAOL) method to exploit common spatial features within attenuation images at different energies and we propose an optimization method which jointly reconstructs the attenuation images at low and high energies with mixed norm regularization on the sparse features obtained by pre-trained convolutional filters through the convolutional analysis operator learning (CAOL) algorithm. Main results. Extensive experiments with simulated and real computed tomography data were performed to validate the effectiveness of the proposed methods, and we report increased reconstruction accuracy compared with CAOL and iterative methods with single and joint total variation regularization. Significance. Qualitative and quantitative results on sparse views and low-dose DECT demonstrate that the proposed MCAOL method outperforms both CAOL applied on each energy independently and several existing state-of-the-art model-based iterative reconstruction techniques, thus paving the way for dose reduction.

Memory-Efficient Training for Fully Unrolled Deep Learned PET Image Reconstruction with Iteration-Dependent Targets

We propose a new version of the forward-backward splitting expectation-maximisation network (FBSEM-Net) along with a new memory-efficient training method enabling the training of fully unrolled implementations of 3D FBSEM-Net. FBSEM-Net unfolds the maximum a posteriori expectation-maximisation algorithm and replaces the regularisation step by a residual convolutional neural network. Both the gradient of the prior and the regularisation strength are learned from training data. In this new implementation, three modifications of the original framework are included. First, iteration-dependent networks are used to have a customised regularisation at each iteration. Second, iteration-dependent targets and losses are introduced so that the regularised reconstruction matches the reconstruction of noise-free data at every iteration. Third, sequential training is performed, making training of large unrolled networks far more memory efficient and feasible. Since sequential training permits unrolling a high number of iterations, there is no need for artificial use of the regularisation step as a leapfrogging acceleration. The results obtained on 2D and 3D simulated data show that FBSEM-Net using iteration-dependent targets and losses improves the consistency in the optimisation of the network parameters over different training runs. We also found that using iteration-dependent targets increases the generalisation capabilities of the network. Furthermore, unrolled networks using iteration-dependent regularisation allowed a slight reduction in reconstruction error compared to using a fixed regularisation network at each iteration. Finally, we demonstrate that sequential training successfully addresses potentially serious memory issues during the training of deep unrolled networks. In particular, it enables the training of 3D fully unrolled FBSEM-Net, not previously feasible, by reducing the memory usage by up to 98% compared to a conventional end-to-end training. We also note that the truncation of the backpropagation (due to sequential training) does not notably impact the network’s performance compared to conventional training with a full backpropagation through the entire network.

A Novel Task-Based reconstruction approach for digital breast tomosynthesis

The reconstruction of a volumetric image from Digital Breast Tomosynthesis (DBT) measurements is an ill-posed inverse problem, for which existing iterative regularized approaches can provide a good solution. However, the clinical task is somehow omitted in the derivation of those techniques, although it plays a primary role in the radiologist diagnosis. In this work, we address this issue by introducing a novel variational formulation for DBT reconstruction, tailored for a specific clinical task, namely the detection of microcalcifications. Our method aims at simultaneously enhancing the detectability performance and enabling a high-quality restoration of the background breast tissues. Our contribution is threefold. First, we introduce an original task-based reconstruction framework through the proposition of a detectability function inspired from mathematical model observers. Second, we propose a novel total-variation regularizer where the gradient field accounts for the different morphological contents of the imaged breast. Third, we integrate the two developed measures into a cost function, minimized thanks to a new form of the Majorize Minimize Memory Gradient (3MG) algorithm. We conduct a numerical comparison of the convergence speed of the proposed method with those of standard convex optimization algorithms. Experimental results show the interest of our DBT reconstruction approach, qualitatively and quantitatively.

PET respiratory motion correction: quo vadis?

Positron emission tomography (PET) respiratory motion correction has been a subject of great interest for the last twenty years, prompted mainly by the development of multimodality imaging devices such as PET/computed tomography (CT) and PET/magnetic resonance imaging (MRI). PET respiratory motion correction involves a number of steps including acquisition synchronization, motion estimation and finally motion correction. The synchronization steps include the use of different external device systems or data driven approaches which have been gaining ground over the last few years. Patient specific or generic motion models using the respiratory synchronized datasets can be subsequently derived and used for correction either in the image space or within the image reconstruction process. Similar overall approaches can be considered and have been proposed for both PET/CT and PET/MRI devices. Certain variations in the case of PET/MRI include the use of MRI specific sequences for the registration of respiratory motion information. The proposed review includes a comprehensive coverage of all these areas of development in field of PET respiratory motion for different multimodality imaging devices and approaches in terms of synchronization, estimation and subsequent motion correction. Finally, a section on perspectives including the potential clinical usage of these approaches is included.

The Evolution of Image Reconstruction in PET: From Filtered Back-Projection to Artificial Intelligence

PET can provide functional images revealing physiologic processes in vivo. Although PET has many applications, there are still some limitations that compromise its precision: the absorption of photons in the body causes signal attenuation; the dead-time limit of system components leads to the loss of the count rate; the scattered and random events received by the detector introduce additional noise; the characteristics of the detector limit the spatial resolution; and the low signal-to-noise ratio caused by the scan-time limit (eg, dynamic scans) and dose concern. The early PET reconstruction methods are analytical approaches based on an idealized mathematical model.

Reconstruction, analysis and interpretation of posterior probability distributions of PET images, using the posterior bootstrap

The uncertainty of reconstructed PET images remains difficult to assess and to interpret for the use in diagnostic and quantification tasks. Here we provide (1) an easy-to-use methodology for uncertainty assessment for almost any Bayesian model in PET reconstruction from single datasets and (2) a detailed analysis and interpretation of produced posterior image distributions. We apply a recent posterior bootstrap framework to the PET image reconstruction inverse problem and obtain simple parallelizable algorithms based on random weights and on existing maximuma posteriori(MAP) (posterior maximum) optimization-based algorithms. Posterior distributions are produced, analyzed and interpreted for several common Bayesian models. Their relationship with the distribution of the MAP image estimate over multiple dataset realizations is exposed. The coverage properties of posterior distributions are validated. More insight is obtained for the interpretation of posterior distributions in order to open the way for including uncertainty information into diagnostic and quantification tasks.

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.

Modeling complex particles phase space with GAN for Monte Carlo SPECT simulations: a proof of concept

A method is proposed to model by a generative adversarial network the distribution of particles exiting a patient during Monte Carlo simulation of emission tomography imaging devices. The resulting compact neural network is then able to generate particles exiting the patient, going towards the detectors, avoiding costly particle tracking within the patient. As a proof of concept, the method is evaluated for single photon emission computed tomography (SPECT) imaging and combined with another neural network modeling the detector response function (ARF-nn). A complete rotating SPECT acquisition can be simulated with reduced computation time compared to conventional Monte Carlo simulation. It also allows the user to perform simulations with several imaging systems or parameters, which is useful for imaging system design.

Improved Low-Count Quantitative PET Reconstruction With an Iterative Neural Network

Image reconstruction in low-count PET is particularly challenging because gammas from natural radioactivity in Lu-based crystals cause high random fractions that lower the measurement signal-to-noise-ratio (SNR). In model-based image reconstruction (MBIR), using more iterations of an unregularized method may increase the noise, so incorporating regularization into the image reconstruction is desirable to control the noise. New regularization methods based on learned convolutional operators are emerging in MBIR. We modify the architecture of an iterative neural network, BCD-Net, for PET MBIR, and demonstrate the efficacy of the trained BCD-Net using XCAT phantom data that simulates the low true coincidence count-rates with high random fractions typical for Y-90 PET patient imaging after Y-90 microsphere radioembolization. Numerical results show that the proposed BCD-Net significantly improves CNR and RMSE of the reconstructed images compared to MBIR methods using non-trained regularizers, total variation (TV) and non-local means (NLM). Moreover, BCD-Net successfully generalizes to test data that differs from the training data. Improvements were also demonstrated for the clinically relevant phantom measurement data where we used training and testing datasets having very different activity distributions and count-levels.

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.

Bootstrap-Optimised Regularised Image Reconstruction for Emission Tomography

In emission tomography, iterative image reconstruction from noisy measured data usually results in noisy images, and so regularisation is often used to compensate for noise. However, in practice, an appropriate, automatic and precise specification of the strength of regularisation for image reconstruction from a given noisy measured dataset remains unresolved. Existing approaches are either empirical approximations with no guarantee of generalisation, or else are computationally intensive cross-validation methods requiring full reconstructions for a limited set of preselected regularisation strengths. In contrast, we propose a novel methodology embedded within iterative image reconstruction, using one or more bootstrapped replicates of the measured data for precise optimisation of the regularisation. The approach uses a conventional unregularised iterative update of a current image estimate from the noisy measured data, and then also uses the bootstrap replicate to obtain a bootstrap update of the current image estimate. The method then seeks the regularisation hyperparameters which, when applied to the bootstrap update of the image, lead to a best fit of the regularised bootstrap update to the conventional measured data update. This corresponds to estimating the degree of regularisation needed in order to map the noisy update to a model of the mean of an ensemble of noisy updates. For a given regularised objective function (e.g. penalised likelihood), no hyperparameter selection or tuning is required. The method is demonstrated for positron emission tomography (PET) data at different noise levels, and delivers near-optimal reconstructions (in terms of reconstruction error) without any knowledge of the ground truth, nor any form of training data.

Multi-exponential Transverse Relaxation Times Estimation from Magnetic Resonance Images under Rician Noise and Spatial Regularization

Relaxation signal inside each voxel of magnetic resonance images (MRI) is commonly fitted by a multi-exponential decay curve. The estimation of a discrete multi-component relaxation model parameters from magnitude MRI data is a challenging nonlinear inverse problem since it should be conducted on the entire image voxels under non-Gaussian noise statistics. This paper proposes an efficient algorithm allowing the joint estimation of relaxation time values and their amplitudes using different criteria taking into account a Rician noise model, combined with a spatial regularization accounting for low spatial variability of relaxation time constants and amplitudes between neighboring voxels. The Rician noise hypothesis is accounted for either by an adapted nonlinear least squares algorithm applied to a corrected least squares criterion or by a majorization-minimization approach applied to the maximum likelihood criterion. In order to solve the resulting large-scale non-negativity constrained optimization problem with a reduced numerical complexity and computing time, an optimization algorithm based on a majorization approach ensuring separability of variables between voxels is proposed. The minimization is carried out iteratively using an adapted Levenberg-Marquardt algorithm that ensures convergence by imposing a sufficient decrease of the objective function and the non-negativity of the parameters. The importance of the regularization alongside the Rician noise incorporation is shown both visually and numerically on a simulated phantom and on magnitude MRI images acquired on fruit samples.

Image domain multi-material decomposition using single energy CT

Multi-material decomposition (MMD) technique decomposes the CT images into basis material images and has been promising in clinical practice for material composition quantification within the human body. MMD could be implemented using the image data acquired from spectral CT or its special case, dual-energy CT (DECT) while the spectral CT data acquisition usually requires a hardware modification. In this paper, we propose an image domain MMD method using single energy CT (SECT). The proposed objective function applies a least square data fidelity term to enforce the minimization between the linear combination of decomposed material image and the measured SECT image, and an edge-preserving (EP) regularization term to meet the piecewise constant property of the material image. We apply the optimization transfer principle to form a pixel-wise separable quadratic surrogate (PWSQS) function in each iteration to decrease the objective function. The pixelwise direct inversion method assisted by the two-material assumption (TMA) is applied to obtain a good initial value. The proposed method is evaluated using a digital phantom, a Catphan phantom and the clinical data. A low-pass filtration method is implemented for a comparison purpose. In the phantom study, the proposed TMA method achieves high volume fraction accuracy (VFA) of 79.64% and the proposed EP method further increases the VFA by 15.56% and decreases the decomposition standard deviation (STD) by 81.51% compared with the TMA method. At the comparable noise level, the proposed EP method increases spatial resolution by an overall factor of 1.01 when the modulation transfer function magnitude is decreased to 50% compared with the low-pass filtration method. In clinical data study, the virtual non-contrast image generated by the proposed method achieves the root-mean-squared-relative error of 2.93% compared with the contrast-free ground-truth image.

PET Reconstruction With Non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence

Standard positron emission tomography (PET) reconstruction techniques are based on maximum-likelihood (ML) optimization methods, such as the maximum-likelihood expectation-maximization (MLEM) algorithm and its variations. Most methodologies rely on a positivity constraint on the activity distribution image. Although this constraint is meaningful from a physical point of view, it can be a source of bias for low-count/high-background PET, which can compromise accurate quantification. Existing methods that allow for negative values in the estimated image usually utilize a modified log-likelihood, and therefore break the data statistics. In this paper, we propose to incorporate the positivity constraint on the projections only, by approximating the (penalized) log-likelihood function by an adequate sequence of objective functions that are easily maximized without constraint. This sequence is constructed such that there is hypo-convergence (a type of convergence that allows the convergence of the maximizers under some conditions) to the original log-likelihood, hence allowing us to achieve maximization with positivity constraint on the projections using simple settings. A complete proof of convergence under weak assumptions is given. We provide results of experiments on simulated data where we compare our methodology with the alternative direction method of multipliers (ADMM) method, showing that our algorithm converges to a maximizer, which stays in the desired feasibility set, with faster convergence than ADMM. We also show that this approach reduces the bias, as compared with MLEM images, in necrotic tumors-which are characterized by cold regions surrounded by hot structures-while reconstructing similar activity values in hot regions.

Probabilistic Graphical Models for Dynamic PET: A Novel Approach to Direct Parametric Map Estimation and Image Reconstruction

In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single-time frames, followed by the application of a suitable kinetic model to time-activity curves (TACs) at the voxel or region-of-interest level. Direct 4D positron emission tomography (PET) reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple time frames within the reconstruction task. Established direct methods are based on a deterministic description of voxelwise TACs, captured by the chosen kinetic model, considering the photon counting process the only source of uncertainty. In this paper, we introduce a new probabilistic modeling strategy based on the key assumption that activity time course would be subject to uncertainty even if the parameters of the underlying dynamic process are known. This leads to a hierarchical model that we formulate using the formalism of probabilistic graphical modeling. The inference is addressed using a new iterative algorithm, in which kinetic modeling results are treated as prior expectation of activity time course, rather than as a deterministic match, making it possible to control the trade-off between a data-driven and a model-driven reconstruction. The proposed method is flexible to an arbitrary choice of (linear and nonlinear) kinetic models, it enables the inclusion of arbitrary (sub)differentiable priors for parametric maps, and it is simple to implement. Computer simulations and an application to a real-patient scan show how the proposed method is able to generalize over conventional indirect and direct approaches, providing a bridge between them by properly tuning the impact of the kinetic modeling step on image reconstruction.

Reduction of beam hardening artifacts on real C-arm CT data using polychromatic statistical image reconstruction

PURPOSE

This work aims at the compensation of beam hardening artifacts by the means of an extended three-dimensional polychromatic statistical reconstruction to be applied for flat panel cone-beam CT.

METHODS

We implemented this reconstruction technique as being introduced by Elbakri et al. (2002) [1] for a multi-GPU system, assuming the underlying object consists of several well-defined materials. Furthermore, we assume one voxel can only contain an overlap of at most two materials, depending on its density value. Given the X-ray spectrum, the procedure enables to reconstruct the energy-dependent attenuation values of the volume.

RESULTS

We evaluated the method by using flat-panel cone-beam CT measurements of structures containing small metal objects and clinical head scan data. In comparison with the water-corrected filtered backprojection, as well as a maximum likelihood reconstruction with a consistency-based beam hardening correction, our method features clearly reduced beam hardening artifacts and a more accurate shape of metal objects.

CONCLUSIONS

Our multi-GPU implementation of the polychromatic reconstruction, which does not require any image pre-segmentation, clearly outperforms the standard reconstructions of objects, with respect to beam hardening even in the presence of metal objects inside the volume. However, remaining artifacts, caused mainly by the limited dynamic range of the detector, may have to be addressed in future work.

Extension of emission expectation maximization lookalike algorithms to Bayesian algorithms

We recently developed a family of image reconstruction algorithms that look like the emission maximum-likelihood expectation-maximization (ML-EM) algorithm. In this study, we extend these algorithms to Bayesian algorithms. The family of emission-EM-lookalike algorithms utilizes a multiplicative update scheme. The extension of these algorithms to Bayesian algorithms is achieved by introducing a new simple factor, which contains the Bayesian information. One of the extended algorithms can be applied to emission tomography and another to transmission tomography. Computer simulations are performed and compared with the corresponding un-extended algorithms. The total-variation norm is employed as the Bayesian constraint in the computer simulations. The newly developed algorithms demonstrate a stable performance. A simple Bayesian algorithm can be derived for any noise variance function. The proposed algorithms have properties such as multiplicative updating, non-negativity, faster convergence rates for bright objects, and ease of implementation. Our algorithms are inspired by Green's one-step-late algorithm. If written in additive-update form, Green's algorithm has a step size determined by the future image value, which is an undesirable feature that our algorithms do not have.

Intercomparison of MR-informed PET image reconstruction methods

PURPOSE

Numerous image reconstruction methodologies for positron emission tomography (PET) have been developed that incorporate magnetic resonance (MR) imaging structural information, producing reconstructed images with improved suppression of noise and reduced partial volume effects. However, the influence of MR structural information also increases the possibility of suppression or bias of structures present only in the PET data (PET-unique regions). To address this, further developments for MR-informed methods have been proposed, for example, through inclusion of the current reconstructed PET image, alongside the MR image, in the iterative reconstruction process. In this present work, a number of kernel and maximum a posteriori (MAP) methodologies are compared, with the aim of identifying methods that enable a favorable trade-off between the suppression of noise and the retention of unique features present in the PET data.

METHODS

The reconstruction methods investigated were: the MR-informed conventional and spatially compact kernel methods, referred to as KEM and KEM largest value sparsification (LVS) respectively; the MR-informed Bowsher and Gaussian MR-guided MAP methods; and the PET-MR-informed hybrid kernel and anato-functional MAP methods. The trade-off between improving the reconstruction of the whole brain region and the PET-unique regions was investigated for all methods in comparison with postsmoothed maximum likelihood expectation maximization (MLEM), evaluated in terms of structural similarity index (SSIM), normalized root mean square error (NRMSE), bias, and standard deviation. Both simulated BrainWeb (10 noise realizations) and real [18 F] fluorodeoxyglucose (FDG) three-dimensional datasets were used. The real [18 F]FDG dataset was augmented with simulated tumors to allow comparison of the reconstruction methodologies for the case of known regions of PET-MR discrepancy and evaluated at full counts (100%) and at a reduced (10%) count level.

RESULTS

For the high-count simulated and real data studies, the anato-functional MAP method performed better than the other methods under investigation (MR-informed, PET-MR-informed and postsmoothed MLEM), in terms of achieving the best trade-off for the reconstruction of the whole brain and PET-unique regions, assessed in terms of the SSIM, NRMSE, and bias vs standard deviation. The inclusion of PET information in the anato-functional MAP method enables the reconstruction of PET-unique regions to attain similarly low levels of bias as unsmoothed MLEM, while moderately improving the whole brain image quality for low levels of regularization. However, for low count simulated datasets the anato-functional MAP method performs poorly, due to the inclusion of noisy PET information in the regularization term. For the low counts simulated dataset, KEM LVS and to a lesser extent, HKEM performed better than the other methods under investigation in terms of achieving the best trade-off for the reconstruction of the whole brain and PET-unique regions, assessed in terms of the SSIM, NRMSE, and bias vs standard deviation.

CONCLUSION

For the reconstruction of noisy data, multiple MR-informed methods produce favorable whole brain vs PET-unique region trade-off in terms of the image quality metrics of SSIM and NRMSE, comfortably outperforming the whole image denoising of postsmoothed MLEM.

Image reconstruction for positron emission tomography based on patch-based regularization and dictionary learning

PURPOSE

Positron emission tomography (PET) is an important tool for nuclear medical imaging. It has been widely used in clinical diagnosis, scientific research, and drug testing. PET is a kind of emission computed tomography. Its basic imaging principle is to use the positron annihilation radiation generated by radionuclide decay to generate gamma photon images. However, in practical applications, due to the low gamma photon counting rate, limited acquisition time, inconsistent detector characteristics, and electronic noise, measured PET projection data often contain considerable noise, which results in ill-conditioned PET images. Therefore, determining how to obtain high-quality reconstructed PET images suitable for clinical applications is a valuable research topic. In this context, this paper presents an image reconstruction algorithm based on patch-based regularization and dictionary learning (DL) called the patch-DL algorithm. Compared to other algorithms, the proposed algorithm can retain more image details while suppressing noise.

METHODS

Expectation-maximization (EM)-like image updating, image smoothing, pixel-by-pixel image fusion, and DL are the four steps of the proposed reconstruction algorithm. We used a two-dimensional (2D) brain phantom to evaluate the proposed algorithm by simulating sinograms that contained random Poisson noise. We also quantitatively compared the patch-DL algorithm with a pixel-based algorithm, a patch-based algorithm, and an adaptive dictionary learning (AD) algorithm.

RESULTS

Through computer simulations, we demonstrated the advantages of the patch-DL method over the pixel-, patch-, and AD-based methods in terms of the tradeoff between noise suppression and detail retention in reconstructed images. Quantitative analysis shows that the proposed method results in a better performance statistically [according to the mean absolute error (MAE), correlation coefficient (CORR), and root mean square error (RMSE)] in considered region of interests (ROI) with two simulated count levels. Additionally, to analyze whether the results among these methods have significant differences, we used one-way analysis of variance (ANOVA) to calculate the corresponding P values. The results show that most of the P < 0.01; some P> 0.01 < 0.05. Therefore, our method can achieve a better quantitative performance than those of traditional methods.

CONCLUSIONS

The results show that the proposed algorithm has the potential to improve the quality of PET image reconstruction. Since the proposed algorithm was validated only with simulated 2D data, it still needs to be further validated with real three-dimensional data. In the future, we intend to explore GPU parallelization technology to further improve the computational efficiency and shorten the computation time.

Dynamic focal plane estimation for dental panoramic radiography

PURPOSE

The digital panoramic radiography is widely used in dental clinics and provides the anatomical information of the intraoral structure along the predefined arc-shaped path. Since the intraoral structure varies depending on the patient, however, it is nearly impossible to design a common and static focal path or plane fitted to the dentition of all patients. In response, we introduce an imaging algorithm for digital panoramic radiography that can provide a focused panoramic radiographic image for all patients, by automatically estimating the best focal plane for each patient.

METHODS

The aim of this study is to improve the image quality of dental panoramic radiography based on a three-dimensional (3D) dynamic focal plane. The plane is newly introduced to represent the arbitrary 3D intraoral structure of each patient. The proposed algorithm consists of three steps: preprocessing, focal plane estimation, and image reconstruction. We first perform preprocessing to improve the accuracy of focal plane estimation. The 3D dynamic focal plane is then estimated by adjusting the position of the image plane so that object boundaries in the neighboring projection data are aligned or focused on the plane. Finally, a panoramic radiographic image is reconstructed using the estimated dynamic focal plane.

RESULTS

The proposed algorithm is evaluated using a numerical phantom dataset and four clinical human datasets. In order to examine the image quality improvement owing to the proposed algorithm, we generate panoramic radiographic images based on a conventional static focal plane and estimated 3D dynamic focal planes, respectively. Experimental results show that the image quality is dramatically improved for all datasets using the 3D dynamic focal planes that are estimated from the proposed algorithm.

CONCLUSIONS

We propose an imaging algorithm for digital panoramic radiography that provides improved image quality by estimating dynamic focal planes fitted to each individual patient's intraoral structure.

Image reconstruction for interrupted-beam x-ray CT on diagnostic clinical scanners

Low-dose x-ray CT is a major research area with high clinical impact. Compressed sensing using view-based sparse sampling and sparsity-promoting regularization has shown promise in simulations, but these methods can be difficult to implement on diagnostic clinical CT scanners since the x-ray beam cannot be switched on and off rapidly enough. An alternative to view-based sparse sampling is interrupted-beam sparse sampling. SparseCT is a recently-proposed interrupted-beam scheme that achieves sparse sampling by blocking a portion of the beam using a multislit collimator (MSC). The use of an MSC necessitates a number of modifications to the standard compressed sensing reconstruction pipeline. In particular, we find that SparseCT reconstruction is feasible within a model-based image reconstruction framework that incorporates data fidelity weighting to consider penumbra effects and source jittering to consider the effect of partial source obstruction. Here, we present these modifications and demonstrate their application in simulations and real-world prototype scans. In simulations compared to conventional low-dose acquisitions, SparseCT is able to achieve smaller normalized root-mean square differences and higher structural similarity measures on two reduction factors. In prototype experiments, we successfully apply our reconstruction modifications and maintain image resolution at quarter-dose reduction level. The SparseCT design requires only small hardware modifications to current diagnostic clinical scanners, opening up new possibilities for CT dose reduction.

Enhancement of Partial Volume Correction in MR-Guided PET Image Reconstruction by Using MRI Voxel Sizes

Positron emission tomography (PET) suffers from poor spatial resolution which results in quantitative bias when evaluating the radiotracer uptake in small anatomical regions, such as the striatum in the brain which is of importance in this paper of neurodegenerative diseases. These partial volume effects need to be compensated for by employing partial volume correction (PVC) methods in order to achieve quantitatively accurate images. Two important PVC methods applied during the reconstruction are resolution modeling, which suffers from Gibbs artifacts, and penalized likelihood using anatomical priors. The introduction of clinical simultaneous PET-MR scanners has attracted new attention for the latter methods and brought new opportunities to use MRI information to assist PET image reconstruction in order to improve image quality. In this context, MR images are usually down-sampled to the PET resolution before being used in MR-guided PET reconstruction. However, the reconstruction of PET images using the MRI voxel size could achieve a better utilization of the high resolution anatomical information and improve the PVC obtained with these methods. In this paper, we evaluate the importance of the use of MRI voxel sizes when reconstructing PET images with MR-guided maximum a posteriori (MAP) methods, specifically the modified Bowsher method. We also propose a method to avoid the artifacts that arise when PET reconstructions are performed in a higher resolution matrix than the standard for a given scanner. The MR-guided MAP reconstructions were implemented with a modified Lange prior that included anatomical information with the Bowsher method. The methods were evaluated with and without resolution modeling for simulated and real brain data. We show that the use of the MRI voxel sizes when reconstructing PET images with MR-guided MAP enhances PVC by improving the contrast and reducing the bias in six different regions of the brain using regional metrics for a single simulated data set and ensemble metrics for ten noise realizations. Similar results were obtained for real data, where a good enhancement of the contrast was achieved. The combination of MR-guided MAP reconstruction with point-spread function modeling and MRI voxel sizes proved to be an attractive method to achieve considerable enhancement of PVC, while reducing and controlling the noise level and Gibbs artifacts.

Multi-modal synergistic PET and MR reconstruction using mutually weighted quadratic priors

PURPOSE

To propose a framework for synergistic reconstruction of PET-MR and multi-contrast MR data to improve the image quality obtained from noisy PET data and from undersampled MR data.

THEORY AND METHODS

Weighted quadratic priors were devised to preserve common boundaries between PET-MR images while reducing noise, PET Gibbs ringing, and MR undersampling artifacts. These priors are iteratively reweighted using normalized multi-modal Gaussian similarity kernels. Synergistic PET-MR reconstructions were built on the PET maximum a posteriori expectation maximization algorithm and the MR regularized sensitivity encoding method. The proposed approach was compared to conventional methods, total variation, and prior-image weighted quadratic regularization methods. Comparisons were performed on a simulated [18 F]fluorodeoxyglucose-PET and T1 /T2 -weighted MR brain phantom, 2 in vivo T1 /T2 -weighted MR brain datasets, and an in vivo [18 F]fluorodeoxyglucose-PET and fluid-attenuated inversion recovery/T1 -weighted MR brain dataset.

RESULTS

Simulations showed that synergistic reconstructions achieve the lowest quantification errors for all image modalities compared to conventional, total variation, and weighted quadratic methods. Whereas total variation regularization preserved modality-unique features, this method failed to recover PET details and was not able to reduce MR artifacts compared to our proposed method. For in vivo MR data, our method maintained similar image quality for 3× and 14× accelerated data. Reconstruction of the PET-MR dataset also demonstrated improved performance of our method compared to the conventional independent methods in terms of reduced Gibbs and undersampling artifacts.

CONCLUSION

The proposed methodology offers a robust multi-modal synergistic image reconstruction framework that can be readily built on existing established algorithms.

Time of flight PET reconstruction using nonuniform update for regional recovery uniformity

PURPOSE

Time of flight (TOF) PET reconstruction is well known to statistically improve the image quality compared to non-TOF PET. Although TOF PET can improve the overall signal to noise ratio (SNR) of the image compared to non-TOF PET, the SNR disparity between separate regions in the reconstructed image using TOF data becomes higher than that using non-TOF data. Using the conventional ordered subset expectation maximization (OS-EM) method, the SNR in the low activity regions becomes significantly lower than in the high activity regions due to the different photon statistics of TOF bins. A uniform recovery across different SNR regions is preferred if it can yield an overall good image quality within small number of iterations in practice. To allow more uniform recovery of regions, a spatially variant update is necessary for different SNR regions.

METHODS

This paper focuses on designing a spatially variant step size and proposes a TOF-PET reconstruction method that uses a nonuniform separable quadratic surrogates (NUSQS) algorithm, providing a straightforward control of spatially variant step size. To control the noise, a spatially invariant quadratic regularization is incorporated, which by itself does not theoretically affect the recovery uniformity. The Nesterov's momentum method with ordered subsets (OS) is also used to accelerate the reconstruction speed. To evaluate the proposed method, an XCAT simulation phantom and clinical data from a pancreas cancer patient with full (ground truth) and 6× downsampled counts were used, where a Poisson thinning process was employed for downsampling. We selected tumor and cold regions of interest (ROIs) and compared the proposed method with the TOF-based conventional OS-EM and OS-SQS algorithms with an early stopping criterion.

RESULTS

In computer simulation, without regularization, hot regions of OS-EM and OS-NUSQS converged similarly, but cold region of OS-EM was noisier than OS-NUSQS after 24 iterations. With regularization, although the overall speeds of OS-EM and OS-NUSQS were similar, recovery ratios of hot and cold regions reconstructed by the OS-NUSQS were more uniform compared to those of the conventional OS-SQS and OS-EM. The OS-NUSQS with Nesterov's momentum converged faster than others while preserving the uniform recovery. In the clinical example, we demonstrated that the OS-NUSQS with Nesterov's momentum provides more uniform recovery ratios of hot and cold ROIs compared to the OS-SQS and OS-EM. Although the cost function of all methods is equivalent, the proposed method has higher structural similarity (SSIM) values of hot and cold regions compared to other methods after 24 iterations. Furthermore, our computing time using graphics processing unit was 80× shorter than the time using quad-core CPUs.

CONCLUSION

This paper proposes a TOF PET reconstruction method using the OS-NUSQS with Nesterov's momentum for uniform recovery of different SNR regions. In particular, the spatially nonuniform step size in the proposed method provides uniform recovery ratios of different SNR regions, and the Nesterov's momentum further accelerates overall convergence while preserving uniform recovery. The computer simulation and clinical example demonstrate that the proposed method converges uniformly across ROIs. In addition, tumor contrast and SSIM of the proposed method were higher than those of the conventional OS-EM and OS-SQS in early iterations.

Multi-Tracer Guided PET Image Reconstruction

Multi-tracer positron emission tomography (PET) has the potential to enhance PET imaging by providing complementary information from different physiological processes. However, one or more of the images may present high levels of noise. Guided image reconstruction methods transfer information from a guide image into the PET image reconstruction to encourage edge-preserving noise reduction. In this work we aim to reduce noise in poorer quality PET datasets via guidance from higher quality ones by using a weighted quadratic penalty approach. In particular, we applied this methodology to [18F]fluorodeoxyglucose (FDG) and [11C]methionine imaging of gliomas. 3D simulation studies showed that guiding the reconstruction of methionine datasets using pre-existing FDG images reduced reconstruction errors across the whole-brain (-8%) and within a tumour (-36%) compared to maximum likelihood expectation-maximisation (MLEM). Furthermore, guided reconstruction outperformed a comparable non-local means filter, indicating that regularising during reconstruction is preferable to post-reconstruction approaches. Hyperparameters selected from the 3D simulation study were applied to real data, where it was observed that the proposed FDG-guided methionine reconstruction allows for better edge preservation and noise reduction than standard MLEM. Overall, the results in this work demonstrate that transferring information between datasets in multi-tracer PET studies improves image quality and quantification performance.

A novel depth-of-interaction rebinning strategy for ultrahigh resolution PET

Small animal positron emission tomography (PET) imaging often requires high resolution (∼few hundred microns) to enable accurate quantitation in small structures such as animal brains. Recently, we have developed a prototype ultrahigh resolution depth-of-interaction (DOI) PET system that uses CdZnTe detectors with a detector pixel size of 350 μm and eight DOI layers with a 250 μm depth resolution. Due to the large number of line-of-response (LOR) combinations of DOIs, the system matrix for reconstruction is 64 times larger than that without DOI. While a high resolution virtual ring geometry can be employed to simplify the system matrix and create a sinogram, the LORs in such a sinogram tend to be sparse and irregular, leading to potential degradation of the reconstructed image quality. In this paper, we propose a novel high resolution sinogram rebinning method in which a uniform sub-sampling DOI strategy is employed. However, even with the high resolution rebinning strategy, the reconstructed image tends to be very noisy due to insufficient photon counts in many high resolution sinogram pixels. To reduce noise effects, we developed a penalized maximum likelihood reconstruction framework with the Poisson log-likelihood and a non-convex total variation penalty. Here, an ordered subsets separable quadratic surrogate and alternating direction method of multipliers are utilized to solve the optimization. To evaluate the performance of the proposed sub-sampling method and the penalized maximum likelihood reconstruction technique, we perform simulations and preliminary point source experiments. By comparing the reconstructed images and profiles based on sinograms without DOI, with rebinned DOI and with sub-sampled DOI, we demonstrate that the proposed method with sub-sampled DOIs can significantly improve the image quality with lower dose and yield a high resolution of  <300 μm.

Cardiac Motion Correction for Helical CT Scan With an Ordinary Pitch

Cardiac X-ray computed tomography (CT) imaging is still challenging due to the cardiac motion during CT scanning, which leads to the presence of motion artifacts in the reconstructed image. In response, many cardiac X-ray CT imaging algorithms have been proposed, based on motion estimation (ME) and motion compensation (MC), to improve the image quality by alleviating the motion artifacts in the reconstructed image. However, these ME/MC algorithms are mainly based on an axial scan or a low-pitch helical scan. In this paper, we propose a ME/MC-based cardiac imaging algorithm for the data set acquired from a helical scan with an ordinary pitch of around 1.0 so as to obtain the whole cardiac image within a single scan of short time without ECG gating. In the proposed algorithm, a sequence of partial angle reconstructed (PAR) images is generated by using consecutive parts of the sinogram, each of which has a small angular span. Subsequently, an initial 4-D motion vector field (MVF) is obtained using multiple pairs of conjugate PAR images. The 4-D MVF is then refined based on an image quality metric so as to improve the quality of the motion-compensated image. Finally, a time-resolved cardiac image is obtained by performing motion-compensated image reconstruction by using the refined 4-D MVF. Using digital XCAT phantom data sets and a human data set commonly obtained via a helical scan with a pitch of 1.0, we demonstrate that the proposed algorithm significantly improves the image quality by alleviating motion artifacts.

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.

A PET reconstruction formulation that enforces non-negativity in projection space for bias reduction in Y-90 imaging

Most existing PET image reconstruction methods impose a nonnegativity constraint in the image domain that is natural physically, but can lead to biased reconstructions. This bias is particularly problematic for Y-90 PET because of the low probability positron production and high random coincidence fraction. This paper investigates a new PET reconstruction formulation that enforces nonnegativity of the projections instead of the voxel values. This formulation allows some negative voxel values, thereby potentially reducing bias. Unlike the previously reported NEG-ML approach that modifies the Poisson log-likelihood to allow negative values, the new formulation retains the classical Poisson statistical model. To relax the non-negativity constraint embedded in the standard methods for PET reconstruction, we used an alternating direction method of multipliers (ADMM). Because choice of ADMM parameters can greatly influence convergence rate, we applied an automatic parameter selection method to improve the convergence speed. We investigated the methods using lung to liver slices of XCAT phantom. We simulated low true coincidence count-rates with high random fractions corresponding to the typical values from patient imaging in Y-90 microsphere radioembolization. We compared our new methods with standard reconstruction algorithms and NEG-ML and a regularized version thereof. Both our new method and NEG-ML allow more accurate quantification in all volumes of interest while yielding lower noise than the standard method. The performance of NEG-ML can degrade when its user-defined parameter is tuned poorly, while the proposed algorithm is robust to any count level without requiring parameter tuning.