Emission Tomography Reconstruction Research Articles

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 at https://github.com/Kuangxd/PETReconstruction.

Refining penalty parameter selection in whole-body PET image reconstruction for lung cancer patients using the cross-validation log-likelihood method

Objective.Penalty parameters in penalized likelihood positron emission tomography (PET) reconstruction are typically determined empirically. The cross-validation log-likelihood (CVLL) method has been introduced to optimize these parameters by maximizing a CVLL function, which assesses the likelihood of reconstructed images using one subset of a list-mode dataset based on another subset. This study aims to validate the efficacy of the CVLL method in whole-body imaging for cancer patients using a conventional clinical PET scanner.Approach.Fifteen lung cancer patients were injected with 243.7 ± 23.8 MBq of [18F]FDG and underwent a 22 min PET scan on a Biograph mCT PET/CT scanner, starting at 60 ± 5 min post-injection. The PET list-mode data were partitioned by subsampling without replacement, with 20 minutes of data for image reconstruction using an in-house ordered subset expectation maximization algorithm and the remaining 2 minutes of data for cross-validation. Two penalty parameters, penalty strengthβand Fair penalty function parameterδ, were subjected to optimization. Whole-body images were reconstructed, and CVLL values were computed across various penalty parameter combinations. The optimal image corresponding to the maximum CVLL value was selected by a grid search for each patient.Main results.Theδvalue required to maximize the CVLL value was notably small (⩽10-6in this study). The influences of voxel size and scan duration on image optimization were investigated. A correlation analysis revealed a significant inverse relationship between optimalβand scan count level, with a correlation coefficient of -0.68 (p-value = 3.5 × 10-5). The optimal images selected by the CVLL method were compared with those chosen by two radiologists based on their diagnostic preferences. Differences were observed in the selection of optimal images.Significance.This study demonstrates the feasibility of incorporating the CVLL method into routine imaging protocols, potentially allowing for a wide range of combinations of injected radioactivity amounts and scan durations in modern PET imaging.

Predicting time-of-flight with Cerenkov light in BGO: a three-stage network approach with multiple timing kernels prior

Objective.In the quest for enhanced image quality in positron emission tomography (PET) reconstruction, the introduction of time-of-flight (TOF) constraints in TOF-PET reconstruction offers superior signal-to-noise ratio. By employing BGO detectors capable of simultaneously emitting prompt Cerenkov light and scintillation light, this approach combines the high time resolution of prompt photons with the high energy resolution of scintillation light, thereby presenting a promising avenue for acquiring more precise TOF information.Approach.In Stage One, we train a raw method capable of predicting TOF information based on coincidence waveform pairs. In Stage Two, the data is categorized into 25 classes based on signal rise time, and the pre-trained raw method is utilized to obtain TOF kernels for each of the 25 classes, thereby generating prior knowledge. Within Stage Three, our proposed deep learning (DL) module, combined with a bias fine-tuning module, utilizes the kernel prior to provide bias compensation values for the data, thereby refining the first-stage outputs and obtaining more accurate TOF predictions.Main results.The three-stage network built upon the LED method resulted in improvements of 11.7 ps and 41.8 ps for full width at half maximum (FWHM) and full width at tenth maximum (FWTM), respectively. Optimal performance was achieved with FWHM of 128.2 ps and FWTM of 286.6 ps when CNN and Transformer were utilized in Stages One and Three, respectively. Further enhancements of 2.3 ps and 3.5 ps for FWHM and FWTM were attained through data augmentation methods.Significance.This study employs neural networks to compensate for the timing delays in mixed (Cerenkov and scintillation photons) signals, combining multiple timing kernels as prior knowledge with DL models. This integration yields optimal predictive performance, offering a superior solution for TOF-PET research utilizing Cerenkov signals.

Transformer-CNN hybrid network for improving PET time of flight prediction

Objective. In positron emission tomography (PET) reconstruction, the integration of time-of-flight (TOF) information, known as TOF-PET, has been a major research focus. Compared to traditional reconstruction methods, the introduction of TOF enhances the signal-to-noise ratio of images. Precision in TOF is measured by full width at half maximum (FWHM) and the offset from ground truth, referred to as coincidence time resolution (CTR) and bias. Approach. This study proposes a network combining transformer and convolutional neural network (CNN) to utilize TOF information from detector waveforms, using event waveform pairs as inputs. This approach integrates the global self-attention mechanism of Transformer, which focuses on temporal relationships, with the local receptive field of CNN. The combination of global and local information allows the network to assign greater weight to the rising edges of waveforms, thereby extracting valuable temporal information for precise TOF predictions. Experiments were conducted using lutetium yttrium oxyorthosilicate (LYSO) scintillators and silicon photomultiplier (SiPM) detectors. The network was trained and tested using the waveform datasets after cropping. Main results. Compared to the constant fraction discriminator (CFD), CNN, CNN with attention, long short-term memory (LSTM) and Transformer, our network achieved an average CTR of 189 ps, reducing it by 82 ps (more than 30%), 13 ps (6.4%), 12 ps (6.0%), 16 ps (7.8%) and 9 ps (4.6%), respectively. Additionally, a reduction of 10.3, 8.7, 6.7 and 4 ps in average bias was achieved compared to CNN, CNN with attention, LSTM and Transformer. Significance. This work demonstrates the potential of applying the Transformer for PET TOF estimation using real experimental data. Through the integration of both CNN and Transformer with local and global attention, it achieves optimal performance, thereby presenting a novel direction for future research in this field.

Deep Image Prior-Based PET Reconstruction From Partial Data

In this paper, we propose an unsupervised deep learning method for positron emission tomography reconstruction (PET) from incomplete data. This method utilizes the so-called deep image prior (DIP) as an untrained deep convolutional neural network (CNN) to generate object reconstructions. The main idea is to re-parameterize the image reconstruction problem as a neural network optimization problem. We show that the proposed method effectively addresses the incomplete data reconstruction problem, which otherwise degrades the image resolution and quality of standard reconstruction algorithms. Meanwhile, the proposed method does not require any pre-training procedures, i.e., it is not biased toward any particular dataset. Hence, it has the potential to be used in clinical situations, where training data would be infeasible or prohibitively expensive. The performance of the proposed approach is evaluated with noisy synthetic data based on shepp-logan and brainweb phantoms, and clinical naive rat data. In addition, robustness studies of the approach with respect to regularization parameters are also carried out. We showcase that the proposed method considerably outperforms the state-of-the-art methods, leading to flexible reconstruction from incomplete PET data.

Inverse radon transform with deep learning: an application in cardiac motion correction

Objective. This paper addresses performing inverse radon transform (IRT) with artificial neural network (ANN) or deep learning, simultaneously with cardiac motion correction (MC). The suggested application domain is cardiac image reconstruction in emission or transmission tomography where IRT is relevant. Our main contribution is in proposing an ANN architecture that is particularly suitable for this purpose. Approach. We validate our approach with two types of datasets. First, we use an abstract object that looks like a heart to simulate motion-blurred radon transform. With the known ground truth in hand, we then train our proposed ANN architecture and validate its effectiveness in MC. Second, we used human cardiac gated datasets for training and validation of our approach. The gating mechanism bins data over time using the electro-cardiogram (ECG) signals for cardiac motion correction. Main results. We have shown that trained ANNs can perform motion-corrected image reconstruction directly from a motion-corrupted sinogram. We have compared our model against two other known ANN-based approaches. Significance. Our method paves the way for eliminating any need for hardware gating in medical imaging.

Spatio-Temporal Positron Emission Tomography Reconstruction with Attenuation and Motion Correction.

The detection of cancer lesions of a comparable size to that of the typical system resolution of modern scanners is a long-standing problem in Positron Emission Tomography. In this paper, the effect of composing an image-registering convolutional neural network with the modeling of the static data acquisition (i.e., the forward model) is investigated. Two algorithms for Positron Emission Tomography reconstruction with motion and attenuation correction are proposed and their performance is evaluated in the detectability of small pulmonary lesions. The evaluation is performed on synthetic data with respect to chosen figures of merit, visual inspection, and an ideal observer. The commonly used figures of merit-Peak Signal-to-Noise Ratio, Recovery Coefficient, and Signal Difference-to-Noise Ration-give inconclusive responses, whereas visual inspection and the Channelised Hotelling Observer suggest that the proposed algorithms outperform current clinical practice.

Exploring the Limitations of Hybrid Adiabatic Quantum Computing for Emission Tomography Reconstruction.

Our study explores the feasibility of quantum computing in emission tomography reconstruction, addressing a noisy ill-conditioned inverse problem. In current clinical practice, this is typically solved by iterative methods minimizing a L2 norm. After reviewing quantum computing principles, we propose the use of a commercially available quantum annealer and employ corresponding hybrid solvers, which combine quantum and classical computing to handle more significant problems. We demonstrate how to frame image reconstruction as a combinatorial optimization problem suited for these quantum annealers and hybrid systems. Using a toy problem, we analyze reconstructions of binary and integer-valued images with respect to their image size and compare them to conventional methods. Additionally, we test our method's performance under noise and data underdetermination. In summary, our method demonstrates competitive performance with traditional algorithms for binary images up to an image size of 32×32 on the toy problem, even under noisy and underdetermined conditions. However, scalability challenges emerge as image size and pixel bit range increase, restricting hybrid quantum computing as a practical tool for emission tomography reconstruction until significant advancements are made to address this issue.

Evaluation of MR anatomically-guided PET reconstruction using a convolutional neural network in PSMA patients.

&#xD;Recently, approaches have utilized the superior anatomical information provided by magnetic resonance imaging (MRI) to guide the reconstruction of positron emission tomography (PET). One of those approaches is the Bowsher's prior, which has been accelerated lately with a convolutional neural network (CNN) to reconstruct MR-guided PET in the imaging domain in routine clinical imaging. Two differently trained Bowsher-CNN methods (B-CNN0 and B-CNN) have been trained and tested on brain PET/MR images on non-PSMA tracers, but so far, have not been evaluated in other anatomical regions yet. &#xD;Methods: &#xD;A NEMA phantom with five of its six spheres filled with the same, calibrated concentration of 18F-DCFPyL-PSMA, and thirty-two patients (mean age 64 ± 7 years) with biopsy-confirmed PCa were used in this study. Reconstruction with either of the two available Bowsher-CNN methods were performed on the conventional MR-based attenuation correction (MRAC) and T1-MR images in the imaging domain. Detectable volume of the spheres and tumors, relative contrast recovery (CR), and background variation (BV) were measured for the MRAC and the Bowsher-CNN images, and qualitative assessment was conducted by ranking the image sharpness and quality by two experienced readers.&#xD;Results: &#xD;For the phantom study, the B-CNN produced 12.7% better CR compared to conventional reconstruction. The small sphere volume (<1.8mL) detectability improved from MRAC to B-CNN by nearly 13%, while measured activity was higher than the ground-truth by 8%. The signal-to-noise ratio (SNR), CR, and BV were significantly improved (p<0.05) in B-CNN images of the tumor. The qualitative analysis determined that tumor sharpness was excellent in 76% of the PET images reconstructed with the B-CNN method, compared to conventional reconstruction. &#xD;Conclusions: &#xD;Applying the MR-guided B-CNN in clinical prostate PET/MR imaging improves some quantitative, as well as qualitative imaging measures. The measured improvements in the phantom are also clearly translated into clinical application.

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.

Neural KEM: A Kernel Method With Deep Coefficient Prior for PET Image Reconstruction.

Image reconstruction of low-count positron emission tomography (PET) data is challenging. Kernel methods address the challenge by incorporating image prior information in the forward model of iterative PET image reconstruction. The kernelized expectation-maximization (KEM) algorithm has been developed and demonstrated to be effective and easy to implement. A common approach for a further improvement of the kernel method would be adding an explicit regularization, which however leads to a complex optimization problem. In this paper, we propose an implicit regularization for the kernel method by using a deep coefficient prior, which represents the kernel coefficient image in the PET forward model using a convolutional neural-network. To solve the maximum-likelihood neural network-based reconstruction problem, we apply the principle of optimization transfer to derive a neural KEM algorithm. Each iteration of the algorithm consists of two separate steps: a KEM step for image update from the projection data and a deep-learning step in the image domain for updating the kernel coefficient image using the neural network. This optimization algorithm is guaranteed to monotonically increase the data likelihood. The results from computer simulations and real patient data have demonstrated that the neural KEM can outperform existing KEM and deep image prior methods.

Q.Clear reconstruction for reducing the scanning time for 68Ga-DOTA-FAPI-04 PET/MR imaging.

This study aims to determine whether Q.Clear positron emission tomography (PET) reconstruction may reduce tracer injection dose or shorten scanning time in 68Gallium-labelled fibroblast activation protein inhibitor (68Ga-FAPI) PET/magnetic resonance (MR) imaging. We retrospectively collected cases of 68Ga-FAPI whole-body imaging performed on integrated PET/MR. PET images were reconstructed using three different methods: ordered subset expectation maximization (OSEM) reconstruction with full scanning time, OSEM reconstruction with half scanning time, and Q.Clear reconstruction with half scanning time. We then measured standardized uptake values (SUVs) within and around lesions, alongside their volumes. We also evaluated image quality using lesion-to-background (L/B) ratio and signal-to-noise ratio (SNR). We then compared these metrics across the three reconstruction techniques using statistical methods. Q.Clear reconstruction significantly increased SUVmax and SUVmean within lesions (more than 30%) and reduced their volumes in comparison with OSEM reconstruction. Background SUVmax also increased significantly, while background SUVmean showed no difference. Average L/B values for Q.Clear reconstruction were only marginally higher than those from OSME reconstruction with half-time. SNR decreased significantly in Q.Clear reconstruction compared with OSEM reconstruction with full time (but not half time). Differences between Q.Clear and OSEM reconstructions in SUVmax and SUVmean values within lesions were significantly correlated with SUVs within lesions. Q.Clear reconstruction was useful for reducing PET injection dose or scanning time while maintaining the image quality. Q.Clear may affect PET quantification, and it is necessary to establish diagnostic recommendations based on Q.Clear results for Q.Clear application.

Unsupervised Bayesian PET Reconstruction

Positron emission tomography (PET) reconstruction has become an ill-posed inverse problem due to low-count projection data, and a robust algorithm is urgently required to improve imaging quality. Recently, the deep image prior (DIP) has drawn much attention and has been successfully applied in several image restoration tasks, such as denoising and inpainting, since it does not need any labels (reference image). However, overfitting is a vital defect of this framework. Hence, many methods have been proposed to mitigate this problem, and DeepRED is a typical representation that combines DIP and regularization by denoising (RED). In this article, we leverage DeepRED from a Bayesian perspective to reconstruct PET images from a single corrupted sinogram without any supervised or auxiliary information. In contrast to the conventional denoisers customarily used in RED, a DnCNN-like denoiser, which can add an adaptive constraint to DIP and facilitate the computation of derivation, is employed. Moreover, to further enhance the regularization, Gaussian noise is injected into the gradient updates, deriving a Markov chain Monte Carlo (MCMC) sampler. Experimental studies on brain and whole-body datasets demonstrate that our proposed method can achieve better performance in terms of qualitative and quantitative results compared to several classic and state-of-the-art methods.

Cross-Attention for Improved Motion Correction in Brain PET.

Head movement during long scan sessions degrades the quality of reconstruction in positron emission tomography (PET) and introduces artifacts, which limits clinical diagnosis and treatment. Recent deep learning-based motion correction work utilized raw PET list-mode data and hardware motion tracking (HMT) to learn head motion in a supervised manner. However, motion prediction results were not robust to testing subjects outside the training data domain. In this paper, we integrate a cross-attention mechanism into the supervised deep learning network to improve motion correction across test subjects. Specifically, cross-attention learns the spatial correspondence between the reference images and moving images to explicitly focus the model on the most correlative inherent information - the head region the motion correction. We validate our approach on brain PET data from two different scanners: HRRT without time of flight (ToF) and mCT with ToF. Compared with traditional and deep learning benchmarks, our network improved the performance of motion correction by 58% and 26% in translation and rotation, respectively, in multi-subject testing in HRRT studies. In mCT studies, our approach improved performance by 66% and 64% for translation and rotation, respectively. Our results demonstrate that cross-attention has the potential to improve the quality of brain PET image reconstruction without the dependence on HMT. All code will be released on GitHub: https://github.com/OnofreyLab/dl_hmc_attention_mlcn2023.

Deep Kernel Representation for Image Reconstruction in PET.

Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate image prior information in the forward model of iterative PET image reconstruction. Existing kernel methods construct the kernels commonly using an empirical process, which may lead to unsatisfactory performance. In this paper, we describe the equivalence between the kernel representation and a trainable neural network model. A deep kernel method is then proposed by exploiting a deep neural network to enable automated learning of an improved kernel model and is directly applicable to single subjects in dynamic PET. The training process utilizes available image prior data to form a set of robust kernels in an optimized way rather than empirically. The results from computer simulations and a real patient dataset demonstrate that the proposed deep kernel method can outperform the existing kernel method and neural network method for dynamic PET image reconstruction.

Dynamic PET Imaging Using Dual Texture Features.

Purpose: This study aims to explore the impact of adding texture features in dynamic positron emission tomography (PET) reconstruction of imaging results.Methods: We have improved a reconstruction method that combines radiological dual texture features. In this method, multiple short time frames are added to obtain composite frames, and the image reconstructed by composite frames is used as the prior image. We extract texture features from prior images by using the gray level-gradient cooccurrence matrix (GGCM) and gray-level run length matrix (GLRLM). The prior information contains the intensity of the prior image, the inverse difference moment of the GGCM and the long-run low gray-level emphasis of the GLRLM.Results: The computer simulation results show that, compared with the traditional maximum likelihood, the proposed method obtains a higher signal-to-noise ratio (SNR) in the image obtained by dynamic PET reconstruction. Compared with similar methods, the proposed algorithm has a better normalized mean squared error (NMSE) and contrast recovery coefficient (CRC) at the tumor in the reconstructed image. Simulation studies on clinical patient images show that this method is also more accurate for reconstructing high-uptake lesions.Conclusion: By adding texture features to dynamic PET reconstruction, the reconstructed images are more accurate at the tumor.

Stochastic EM methods with variance reduction for penalised PET reconstructions

Expectation-maximisation (EM) is a popular and well-established method for image reconstruction in positron emission tomography (PET) but it often suffers from slow convergence. Ordered subset EM (OSEM) is an effective reconstruction algorithm that provides significant acceleration during initial iterations, but it has been observed to enter a limit cycle. In this work, we investigate two classes of algorithms for accelerating OSEM based on variance reduction for penalised PET reconstructions. The first is a stochastic variance reduced EM algorithm, termed as SVREM, an extension of the classical EM to the stochastic context that combines classical OSEM with variance reduction techniques for gradient descent. The second views OSEM as a preconditioned stochastic gradient ascent, and applies variance reduction techniques, i.e., SAGA and SVRG, to estimate the update direction. We present several numerical experiments to illustrate the efficiency and accuracy of the approaches. The numerical results show that these approaches significantly outperform existing OSEM type methods for penalised PET reconstructions, and hold great potential.

MRI-aided kernel PET image reconstruction method based on texture features

We investigate the reconstruction of low-count positron emission tomography (PET) projection, which is an important, but challenging, task. Using the texture feature extraction method of radiomics, i.e. the gray-level co-occurrence matrix (GLCM), texture features can be extracted from magnetic resonance imaging images with high-spatial resolution. In this work, we propose a kernel reconstruction method combining autocorrelation texture features derived from the GLCM. The new kernel function includes the correlations of both the intensity and texture features from the prior image. By regarding the GLCM as a discrete approximation of a probability density function, the asymptotically gray-level-invariant autocorrelation texture feature is generated, which can maintain the accuracy of texture features extracted from small image regions by reducing the number of quantized image gray levels. A computer simulation shows that the proposed method can effectively reduce the noise in the reconstructed image compared to the maximum likelihood expectation maximum method and improve the image quality and tumor region accuracy compared to the original kernel method for low-count PET reconstruction. A simulation study on clinical patient images also shows that the proposed method can improve the whole image quality and that the reconstruction of a high-uptake lesion is more accurate than that achieved by the original kernel method.

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.

Robust compartmental model fitting in direct emission tomography reconstruction

Dynamic tomography reconstructs a time activity curve (TAC) for every voxel assuming that the algebraic form of the function is known a priori. The algebraic form derived from the analysis of compartmental models depends nonlinearly on the nonnegative parameters to be determined. Direct methods apply fitting in every iteration step. Because of the iterative nature of the maximum likelihood–expectation maximization (ML–EM) reconstruction, the fitting result of the previous step can serve as a good starting point in the current step; thus, after the first iteration we have a guess that is not far from the solution, which allows the use of gradient-based local optimization methods. However, finding good initial guesses for the first ML–EM iteration is a critical problem since gradient-based local optimization algorithms do not guarantee convergence to the global optimum if they are started at an inappropriate location. This paper examines the robust solution of the fitting problem both in the initial phase and during the ML–EM iteration. This solution is implemented on GPUs and is built into the 4D reconstruction module of the TeraTomo software.