PET Reconstruction With an Anatomical MRI Prior Using Parallel Level Sets

Resolution enhancement, noise suppression, and joint T2* decay estimation in dual-echo sodium-23 MR imaging using anatomically guided reconstruction

PURPOSE

Sodium MRI is challenging because of the low tissue concentration of the 23 Na nucleus and its extremely fast biexponential transverse relaxation rate. In this article, we present an iterative reconstruction framework using dual-echo 23 Na data and exploiting anatomical prior information (AGR) from high-resolution, low-noise, 1 H MR images. This framework enables the estimation and modeling of the spatially varying signal decay due to transverse relaxation during readout (AGRdm), which leads to images of better resolution and reduced noise resulting in improved quantification of the reconstructed 23 Na images.

METHODS

The proposed framework was evaluated using reconstructions of 30 noise realizations of realistic simulations of dual echo twisted projection imaging (TPI) 23 Na data. Moreover, three dual echo 23 Na TPI brain datasets of healthy controls acquired on a 3T Siemens Prisma system were reconstructed using conventional reconstruction, AGR and AGRdm.

RESULTS

Our simulations show that compared to conventional reconstructions, AGR and AGRdm show improved bias-noise characteristics in several regions of the brain. Moreover, AGR and AGRdm images show more anatomical detail and less noise in the reconstructions of the experimental data sets. Compared to AGR and the conventional reconstruction, AGRdm shows higher contrast in the sodium concentration ratio between gray and white matter and between gray matter and the brain stem.

CONCLUSION

AGR and AGRdm generate 23 Na images with high resolution, high levels of anatomical detail, and low levels of noise, potentially enabling high-quality 23 Na MR imaging at 3T.

M3S-Net: multi-modality multi-branch multi-self-attention network with structure-promoting loss for low-dose PET/CT enhancement

Objective.PET (Positron Emission Tomography) inherently involves radiotracer injections and long scanning time, which raises concerns about the risk of radiation exposure and patient comfort. Reductions in radiotracer dosage and acquisition time can lower the potential risk and improve patient comfort, respectively, but both will also reduce photon counts and hence degrade the image quality. Therefore, it is of interest to improve the quality of low-dose PET images.Approach.A supervised multi-modality deep learning model, named M3S-Net, was proposed to generate standard-dose PET images (60 s per bed position) from low-dose ones (10 s per bed position) and the corresponding CT images. Specifically, we designed a multi-branch convolutional neural network with multi-self-attention mechanisms, which first extracted features from PET and CT images in two separate branches and then fused the features to generate the final generated PET images. Moreover, a novel multi-modality structure-promoting term was proposed in the loss function to learn the anatomical information contained in CT images.Main results.We conducted extensive numerical experiments on real clinical data collected from local hospitals. Compared with state-of-the-art methods, the proposed M3S-Net not only achieved higher objective metrics and better generated tumors, but also performed better in preserving edges and suppressing noise and artifacts.Significance.The experimental results of quantitative metrics and qualitative displays demonstrate that the proposed M3S-Net can generate high-quality PET images from low-dose ones, which are competable to standard-dose PET images. This is valuable in reducing PET acquisition time and has potential applications in dynamic PET imaging.

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

Background. 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 with non-PSMA tracers, but so far, have not been evaluated in other anatomical regions yet.Methods. 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.Results. For the phantom study, the B-CNN produced 12.7% better CR compared to conventional reconstruction. The small sphere volume (<1.8 ml) 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, 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.Conclusions. 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.

Fast and memory-efficient reconstruction of sparse Poisson data in listmode with non-smooth priors with application to time-of-flight PET

Objective. Complete time of flight (TOF) sinograms of state-of-the-art TOF PET scanners have a large memory footprint. Currently, they contain ∼4 · 109 data bins which amount to ∼17 GB in 32 bit floating point precision. Moreover, their size will continue to increase with advances in the achievable detector TOF resolution and increases in the axial field of view. Using iterative algorithms to reconstruct such enormous TOF sinograms becomes increasingly challenging due to the memory requirements and the computation time needed to evaluate the forward model for every data bin. This is especially true for more advanced optimization algorithms such as the stochastic primal-dual hybrid gradient (SPDHG) algorithm which allows for the use of non-smooth priors for regularization using subsets with guaranteed convergence. SPDHG requires the storage of additional sinograms in memory, which severely limits its application to data sets from state-of-the-art TOF PET systems using conventional computing hardware. Approach. Motivated by the generally sparse nature of the TOF sinograms, we propose and analyze a new listmode (LM) extension of the SPDHG algorithm for image reconstruction of sparse data following a Poisson distribution. The new algorithm is evaluated based on realistic 2D and 3D simulationsn, and a real data set acquired on a state-of-the-art TOF PET/CT system. The performance of the newly proposed LM SPDHG algorithm is compared against the conventional sinogram SPDHG and the listmode EM-TV algorithm. Main results. We show that the speed of convergence of the proposed LM-SPDHG is equivalent the original SPDHG operating on binned data (TOF sinograms). However, we find that for a TOF PET system with 400 ps TOF resolution and 25 cm axial FOV, the proposed LM-SPDHG reduces the required memory from approximately 56 to 0.7 GB for a short dynamic frame with 107 prompt coincidences and to 12.4 GB for a long static acquisition with 5·108 prompt coincidences. Significance. In contrast to SPDHG, the reduced memory requirements of LM-SPDHG enables a pure GPU implementation on state-of-the-art GPUs—avoiding memory transfers between host and GPU—which will substantially accelerate reconstruction times. This in turn will allow the application of LM-SPDHG in routine clinical practice where short reconstruction times are crucial.

Enhancing the spatial resolution of hyperpolarized carbon-13 MRI of human brain metabolism using structure guidance

PURPOSE

Dynamic nuclear polarization is an emerging imaging method that allows noninvasive investigation of tissue metabolism. However, the relatively low metabolic spatial resolution that can be achieved limits some applications, and improving this resolution could have important implications for the technique.

METHODS

We propose to enhance the 3D resolution of carbon-13 magnetic resonance imaging (13 C-MRI) using the structural information provided by hydrogen-1 MRI (1 H-MRI). The proposed approach relies on variational regularization in 3D with a directional total variation regularizer, resulting in a convex optimization problem which is robust with respect to the parameters and can efficiently be solved by many standard optimization algorithms. Validation was carried out using an in silico phantom, an in vitro phantom and in vivo data from four human volunteers.

RESULTS

The clinical data used in this study were upsampled by a factor of 4 in-plane and by a factor of 15 out-of-plane, thereby revealing occult information. A key finding is that 3D super-resolution shows superior performance compared to several 2D super-resolution approaches: for example, for the in silico data, the mean-squared-error was reduced by around 40% and for all data produced increased anatomical definition of the metabolic imaging.

CONCLUSION

The proposed approach generates images with enhanced anatomical resolution while largely preserving the quantitative measurements of metabolism. Although the work requires clinical validation against tissue measures of metabolism, it offers great potential in the field of 13 C-MRI and could significantly improve image quality in the future.

Multispectral interlaced sparse sampling photoacoustic tomography based on directional total variation

BACKGROUND AND OBJECTIVE

Photoacoustic tomography (PAT) is capable of obtaining cross-sectional images of small animals that represent the optical absorption of biological tissues. The multispectral Interlaced Sparse Sampling PAT, or ISS-PAT, is a previously proposed PAT imaging method that offered high quality images with much sparser transducer angular coverage. Although it provides superior imaging performance, the original ISS-PAT method suffered from a heavy computation burden, which hinders its practical application.

METHODS

Here, we propose a new regularization scheme based on the directional total variation (dTV) for ISS-PAT. This method efficiently imposes the structural information by considering both the edge position and direction information of the anatomical prior image in ISS-PAT. It does not require image segmentation, and can be conveniently solved by a modified alternating direction of multipliers (ADMM) algorithm.

RESULTS

We perform simulation, tissue mimicking phantom and in vivo small animal experiments to evaluate the proposed scheme. The reconstructed PAT images showed image quality and spectral un-mixing accuracy close to those obtained by non-local means based ISS-PAT, but with much shorter image reconstruction time. For a 1/6 sparse sampling rate, the average efficiency improvement is nearly 16-folds.

CONCLUSIONS

The experimental results demonstrate the feasibility of the dTV regularization scheme for ISS-PAT. Its efficient image reconstruction performance facilitates the potential of the hardware realization and practical applications of the ISS-PAT.

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.

Dynamic PET image reconstruction incorporating a median nonlocal means kernel method

In dynamic positron emission tomography (PET) imaging, the reconstructed image of a single frame often exhibits high noise due to limited counting statistics of projection data. This study proposed a median nonlocal means (MNLM)-based kernel method for dynamic PET image reconstruction. The kernel matrix is derived from median nonlocal means of pre-reconstructed composite images. Then the PET image intensities in all voxels were modeled as a kernel matrix multiplied by coefficients and incorporated into the forward model of PET projection data. Then, the coefficients of each feature were estimated by the maximum likelihood method. Using simulated low-count dynamic data of Zubal head phantom, the quantitative performance of the proposed MNLM kernel method was investigated and compared with the maximum-likelihood method, conventional kernel method with and without median filter, and nonlocal means (NLM) kernel method. Simulation results showed that the MNLM kernel method achieved visual and quantitative accuracy improvements (in terms of the ensemble mean squared error, bias versus variance, and contrast versus noise performances). Especially for frame 2 with the lowest count level of a single frame, the MNLM kernel method achieves lower ensemble mean squared error (10.43%) than the NLM kernel method (13.68%), conventional kernel method with and without median filter (11.88% and 23.50%), and MLEM algorithm (24.77%). The study on real low-dose ¹⁸F-FDG rat data also showed that the MNLM kernel method outperformed other methods in visual and quantitative accuracy improvements (in terms of regional noise versus intensity mean performance).

A Novel Combined Level Set Model for Carpus Segmentation from Magnetic Resonance Images with Prior Knowledge aligned in Polar Coordinate System

BACKGROUND AND OBJECTIVE

Segmentation on carpus provides essential information for clinical applications including pathological evaluations, therapy planning, wrist biomechanical analysis, etc. Along with the acquisition procedure of magnetic resonance (MR) technique, poor quality of wrist images (e.g., occlusion, low signal-to-noise ratio, and contrast) often causes segmentation failure.

METHODS

In this work, to address such problems, a shape prior enhanced level set model was proposed. By transferring a shape contour in Cartesian Coordinate System (COS) into a curve in Polar Coordinate System (POS), parameters describing conventional shape invariance, i.e., translations, rotation, and scale were simplified into a single parameter for phase shift, which strongly improved algorithm efficiency. Given a training set in COS, a confidence interval representing the corresponding curves in POS was utilized as the shape prior set term in the model. Integrated with an edge detector, a local intensity descriptor, and a regularization term, the proposed method further possessed abilities against noise, intensity inhomogeneity as well as re-initialization problem. Images from 15 in-vivo acquired MR-datasets of the human wrist were used for validation. The performance of the proposed method has been compared with three state-of-the-art methods.

RESULTS

We reported a Dice Similarity Coefficient of 96.88±1.20%, a Relative Volume Difference of -1.53±3.01%, a Volume Overlap Error of 6.03±2.23%, a 95% Hausdorff Distance of 1.43±0.66 mm, an Average Symmetric Surface Distance of 0.50±0.17 mm, and a Root Mean Square Distance of 0.71±0.25 mm for the proposed method. The time consumption was 36.03±19.98 s.

CONCLUSIONS

Experimental results indicated that, compared with three other methods, the proposed method achieved significant improvement in terms of accuracy and efficiency.

Core Imaging Library - Part II: multichannel reconstruction for dynamic and spectral tomography

The newly developed core imaging library (CIL) is a flexible plug and play library for tomographic imaging with a specific focus on iterative reconstruction. CIL provides building blocks for tailored regularized reconstruction algorithms and explicitly supports multichannel tomographic data. In the first part of this two-part publication, we introduced the fundamentals of CIL. This paper focuses on applications of CIL for multichannel data, e.g. dynamic and spectral. We formalize different optimization problems for colour processing, dynamic and hyperspectral tomography and demonstrate CIL's capabilities for designing state-of-the-art reconstruction methods through case studies and code snapshots. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.

Motion estimation and correction for simultaneous PET/MR using SIRF and CIL

SIRF is a powerful PET/MR image reconstruction research tool for processing data and developing new algorithms. In this research, new developments to SIRF are presented, with focus on motion estimation and correction. SIRF's recent inclusion of the adjoint of the resampling operator allows gradient propagation through resampling, enabling the MCIR technique. Another enhancement enabled registering and resampling of complex images, suitable for MRI. Furthermore, SIRF's integration with the optimization library CIL enables the use of novel algorithms. Finally, SPM is now supported, in addition to NiftyReg, for registration. Results of MR and PET MCIR reconstructions are presented, using FISTA and PDHG, respectively. These demonstrate the advantages of incorporating motion correction and variational and structural priors. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.

Synergistic multi-spectral CT reconstruction with directional total variation

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel. We propose to fuse these available data (represented by a single sinogram) to obtain a polyenergetic image which keeps structural information shared by the energy channels with increased signal-to-noise ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyse the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.

Deconvolution-based partial volume correction of PET images with parallel level set regularization

The partial volume effect (PVE), caused by the limited spatial resolution of positron emission tomography (PET), degrades images both qualitatively and quantitatively. Anatomical information provided by magnetic resonance (MR) images has the potential to play an important role in partial volume correction (PVC) methods. Post-reconstruction MR-guided PVC methods typically use segmented MR tissue maps, and further, assume that PET activity distribution is uniform in each region, imposing considerable constraints through anatomical guidance. In this work, we present a post-reconstruction PVC method based on deconvolution with parallel level set (PLS) regularization. We frame the problem as an iterative deconvolution task with PLS regularization that incorporates anatomical information without requiring MR segmentation or assuming uniformity of PET distributions within regions. An efficient algorithm for non-smooth optimization of the objective function (invoking split Bregman framework) is developed so that the proposed method can be feasibly applied to 3D images and produces sharper images compared to PLS method with smooth optimization. The proposed method was evaluated together with several other PVC methods using both realistic simulation experiments based on the BrainWeb phantom as well asin vivohuman data. Our proposed method showed enhanced quantitative performance when realistic MR guidance was provided. Further, the proposed method is able to reduce image noise while preserving structure details onin vivohuman data, and shows the potential to better differentiate amyloid positive and amyloid negative scans. Overall, our results demonstrate promise to provide superior performance in clinical imaging scenarios.

Anatomy-guided PET reconstruction usingl1bowsher prior

Advances in simultaneous positron emission tomography/magnetic resonance imaging (PET/MRI) technology have led to an active investigation of the anatomy-guided regularized PET image reconstruction algorithm based on MR images. Among the various priors proposed for anatomy-guided regularized PET image reconstruction, Bowsher's method based on second-order smoothing priors sometimes suffers from over-smoothing of detailed structures. Therefore, in this study, we propose a Bowsher prior based on thel1-norm and an iteratively reweighting scheme to overcome the limitation of the original Bowsher method. In addition, we have derived a closed solution for iterative image reconstruction based on this non-smooth prior. A comparison study between the originall2and proposedl1Bowsher priors was conducted using computer simulation and real human data. In the simulation and real data application, small lesions with abnormal PET uptake were better detected by the proposedl1Bowsher prior methods than the original Bowsher prior. The originall2Bowsher leads to a decreased PET intensity in small lesions when there is no clear separation between the lesions and surrounding tissue in the anatomical prior. However, the proposedl1Bowsher prior methods showed better contrast between the tumors and surrounding tissues owing to the intrinsic edge-preserving property of the prior which is attributed to the sparseness induced byl1-norm, especially in the iterative reweighting scheme. Besides, the proposed methods demonstrated lower bias and less hyper-parameter dependency on PET intensity estimation in the regions with matched anatomical boundaries in PET and MRI. Therefore, these methods will be useful for improving the PET image quality based on the anatomical side information.

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.

Di-chromatic interpolation of magnetic resonance metabolic images

OBJECTIVE

Magnetic resonance imaging with hyperpolarized contrast agents can provide unprecedented in vivo measurements of metabolism, but yields images that are lower resolution than that achieved with proton anatomical imaging. In order to spatially localize the metabolic activity, the metabolic image must be interpolated to the size of the proton image. The most common methods for choosing the unknown values rely exclusively on values of the original uninterpolated image.

METHODS

In this work, we present an alternative method that uses the higher-resolution proton image to provide additional spatial structure. The interpolated image is the result of a convex optimization algorithm which is solved with the fast iterative shrinkage threshold algorithm (FISTA).

RESULTS

Results are shown with images of hyperpolarized pyruvate, lactate, and bicarbonate using data of the heart and brain from healthy human volunteers, a healthy porcine heart, and a human with prostate cancer.

Quantitative bone SPECT/CT reconstruction utilizing anatomical information

Background

Bone SPECT/CT has been shown to offer superior sensitivity and specificity compared to conventional whole-body planar scanning. Furthermore, bone SPECT/CT allows quantitative imaging, which is challenging with planar methods. In order to gain better quantitative accuracy, Bayesian reconstruction algorithms, including both image derived and anatomically guided priors, have been utilized in reconstruction in PET/CT scanning, but they have not been widely used in SPECT/CT studies. Therefore, the aim of this work was to evaluate the performance of CT-guided reconstruction in quantitative bone SPECT.

Methods

Three Bayesian reconstruction methods were evaluated against the conventional ordered subsets expectation maximization (OSEM) reconstruction method. One of the studied Bayesian methods was the relative difference prior (RDP), which has recently gained popularity in PET reconstruction. The other two methods, anatomically guided smoothing prior (AMAP-S) and anatomically guided relative difference prior (AMAP-R), utilized anatomical information from the CT scan. The reconstruction methods were evaluated in terms of quantitative accuracy with artificial lesions inserted in clinical patient studies and with 20 real clinical patients. Maximum and mean standardized uptake values (SUVs) of the lesions were defined.

Results

The analyses showed that all studied Bayesian methods performed better than OSEM and the anatomical priors also outperformed RDP. The average relative error in mean SUV for the artificial lesion study for OSEM, RDP, AMAP-S, and AMAP-R was − 53%, − 35%, − 15%, and − 10%, when the CT study had matching lesions. In the patient study, the RDP method gave 16 ± 9% higher maximum SUV values than OSEM, while AMAP-S and AMAP-R offered increases of 36 ± 8% and 36 ± 9%, respectively. Mean SUV increased for RDP, AMAP-S, and AMAP-R by 18 ± 9%, 26 ± 5%, and 33 ± 5% when compared to OSEM.

Conclusions

The Bayesian methods with anatomical prior, especially the relative difference prior-based method (AMAP-R), outperformed OSEM and reconstruction without anatomical prior in terms of quantitative accuracy.

Approximating anatomically-guided PET reconstruction in image space using a convolutional neural network

In the last two decades, it has been shown that anatomically-guided PET reconstruction can lead to improved bias-noise characteristics in brain PET imaging. However, despite promising results in simulations and first studies, anatomically-guided PET reconstructions are not yet available for use in routine clinical because of several reasons. In light of this, we investigate whether the improvements of anatomically-guided PET reconstruction methods can be achieved entirely in the image domain with a convolutional neural network (CNN). An entirely image-based CNN post-reconstruction approach has the advantage that no access to PET raw data is needed and, moreover, that the prediction times of trained CNNs are extremely fast on state of the art GPUs which will substantially facilitate the evaluation, fine-tuning and application of anatomically-guided PET reconstruction in real-world clinical settings. In this work, we demonstrate that anatomically-guided PET reconstruction using the asymmetric Bowsher prior can be well-approximated by a purely shift-invariant convolutional neural network in image space allowing the generation of anatomically-guided PET images in almost real-time. We show that by applying dedicated data augmentation techniques in the training phase, in which 16 [18F]FDG and 10 [18F]PE2I data sets were used, lead to a CNN that is robust against the used PET tracer, the noise level of the input PET images and the input MRI contrast. A detailed analysis of our CNN in 36 [18F]FDG, 18 [18F]PE2I, and 7 [18F]FET test data sets demonstrates that the image quality of our trained CNN is very close to the one of the target reconstructions in terms of regional mean recovery and regional structural similarity.

Technical Note: Ultra high-resolution radiotracer-specific digital pet brain phantoms based on the BigBrain atlas

PURPOSE

To introduce a method that allows the generation of ultra high-resolution (submillimeter) heterogeneous digital PET brain phantoms and to provide a new publicly available [18 F ]FDG phantom as an example.

METHOD

The radiotracer distribution of the phantom is estimated by minimizing the Kullback-Leibler distance between the parameterized unknown phantom distribution and a radiotracer-specific template used as a reference. The phantom is modelled using the histological and tissue classified volumes of the BigBrain atlas to provide both high resolution and heterogeneity. The Hammersmith brain atlas is also included to allow the estimation of different activity values in different anatomical regions of the brain. Using this method, a realistic [18 F ]FDG phantom was produced, where a single real [18 F ]FDG scan was used as the reference to match. An MRI T1-weighted image, obtained from the BigBrain atlas, and a pseudo-CT are included to complete the dataset. A full PET-MRI dataset was simulated and reconstructed with MR-guided methods for the new [18 F ]FDG phantom.

RESULTS

An ultra high-resolution (400 μm voxel size) and heterogeneous phantom for [18 F ]FDG was obtained. The radiotracer activity follows the patterns observed in the scan used as a reference. The simulated PET-MRI dataset provided a realistic simulation that was able to be reconstructed with MR-guided methods. By visual inspection, the reconstructed images showed similar patterns to the real data and the improvements in contrast and noise with respect to the standard MLEM reconstruction were more modest compared to simulations done with a simpler phantom, which was created from the same MRI image used to assist the reconstruction.

CONCLUSIONS

A method to create high-resolution heterogeneous digital brain phantoms for different PET radiotracers has been presented and successfully employed to create a new publicly available [18 F ]FDG phantom. The generated phantom is of high resolution, is heterogeneous, and simulates the uptake of the radiotracer in the different regions of the brain.

Super-Resolution PET Imaging Using Convolutional Neural Networks

Positron emission tomography (PET) suffers from severe resolution limitations which reduce its quantitative accuracy. In this paper, we present a super-resolution (SR) imaging technique for PET based on convolutional neural networks (CNNs). To facilitate the resolution recovery process, we incorporate high-resolution (HR) anatomical information based on magnetic resonance (MR) imaging. We introduce the spatial location information of the input image patches as additional CNN inputs to accommodate the spatially-variant nature of the blur kernels in PET. We compared the performance of shallow (3-layer) and very deep (20-layer) CNNs with various combinations of the following inputs: low-resolution (LR) PET, radial locations, axial locations, and HR MR. To validate the CNN architectures, we performed both realistic simulation studies using the BrainWeb digital phantom and clinical studies using neuroimaging datasets. For both simulation and clinical studies, the LR PET images were based on the Siemens HR+ scanner. Two different scenarios were examined in simulation: one where the target HR image is the ground-truth phantom image and another where the target HR image is based on the Siemens HRRT scanner - a high-resolution dedicated brain PET scanner. The latter scenario was also examined using clinical neuroimaging datasets. A number of factors affected relative performance of the different CNN designs examined, including network depth, target image quality, and the resemblance between the target and anatomical images. In general, however, all deep CNNs outperformed classical penalized deconvolution and partial volume correction techniques by large margins both qualitatively (e.g., edge and contrast recovery) and quantitatively (as indicated by three metrics: peak signal-to-noise-ratio, structural similarity index, and contrast-to-noise ratio).

Benefits of Using a Spatially-Variant Penalty Strength With Anatomical Priors in PET Reconstruction

In this study, we explore the use of a spatially-variant penalty strength in penalized image reconstruction using anatomical priors to reduce the dependence of lesion contrast on surrounding activity and lesion location. This work builds on a previous method to make the local perturbation response (LPR) approximately spatially invariant. While the dependence of lesion contrast on the local properties introduced by the anatomical penalty is intentional, the method aims to reduce the influence from surroundings lying along the lines of response (LORs) but not in the penalty neighborhood structure. The method is evaluated using simulated data, assuming that the anatomical information is absent or well-aligned with the corresponding activity images. Since the parallel level sets (PLS) penalty is convex and has shown promising results in the literature, it is chosen as the representative anatomical penalty and incorporated into the previously proposed preconditioned algorithm (L-BFGS-B-PC) for achieving good image quality and fast convergence rate. A 2D disc phantom with a feature at the center and a 3D XCAT thorax phantom with lesions inserted in different slices are used to study how surrounding activity and lesion location affect the visual appearance and quantitative consistency. A bias and noise analysis is also performed with the 2D disc phantom. The consistency of the algorithm convergence rate with respect to different data noise and background levels is also investigated using the XCAT phantom. Finally, an example of reconstruction for a patient dataset with inserted pseudo lesions is used as a demonstration in a clinical context. We show that applying the spatially-variant penalization with PLS can reduce the dependence of the lesion contrast on the surrounding activity and lesion location. It does not affect the bias and noise trade-off curves for matched local resolution. Moreover, when using the proposed penalization, significant improvement in algorithm convergence rate and convergence consistency is observed.

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

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

Iterative PET Image Reconstruction Using Convolutional Neural Network Representation

PET image reconstruction is challenging due to the ill-poseness of the inverse problem and limited number of detected photons. Recently, the deep neural networks have been widely and successfully used in computer vision tasks and attracted growing interests in medical imaging. In this paper, we trained a deep residual convolutional neural network to improve PET image quality by using the existing inter-patient information. An innovative feature of the proposed method is that we embed the neural network in the iterative reconstruction framework for image representation, rather than using it as a post-processing tool. We formulate the objective function as a constrained optimization problem and solve it using the alternating direction method of multipliers algorithm. Both simulation data and hybrid real data are used to evaluate the proposed method. Quantification results show that our proposed iterative neural network method can outperform the neural network denoising and conventional penalized maximum likelihood methods.

Magnetic Resonance Fingerprinting: Implications and Opportunities for PET/MR

Magnetic Resonance Imaging (MRI) can be used to assess anatomical structure, and its sensitivity to a variety of tissue properties enables superb contrast between tissues as well as the ability to characterize these tissues. However, despite vast potential for quantitative and functional evaluation, MRI is typically used qualitatively, in which the underlying tissue properties are not measured, and thus the brightness of each pixel is not quantitatively meaningful. Positron Emission Tomography (PET) is an inherently quantitative imaging modality that interrogates functional activity within a tissue, probed by a molecule of interest coupled with an appropriate tracer. These modalities can complement one another to provide clinical information regarding both structure and function, but there are still technical and practical hurdles in the way of the integrated use of both modalities. Recent advances in MRI have moved the field in an increasingly quantitative direction, which is complementary to PET, and could also potentially help solve some of the challenges in PET/MR. Magnetic Resonance Fingerprinting (MRF) is a recently described MRI-based technique which can efficiently and simultaneously quantitatively map several tissue properties in a single exam. Here, the basic principles behind the quantitative approach of MRF are laid out, and the potential implications for combined PET/MR are discussed.

Effect of PET-MR Inconsistency in the Kernel Image Reconstruction Method

Anatomically-driven image reconstruction algorithms have become very popular in positron emission tomography (PET) where they have demonstrated improved image resolution and quantification. This work, consider the effect of spatial inconsistency between MR and PET images in hot and cold regions of the PET image. We investigate these effects on the kernel method from machine learning, in particular, the hybrid kernelized expectation maximization (HKEM). These were applied to Jaszczak phantom and patient data acquired with the Biograph Siemens mMR. The results show that even a small shift can cause a significant change in activity concentration. In general, the PET-MR inconsistencies can induce the partial volume effect, more specifically the 'spill-in' of the affected cold regions and the 'spill-out' from the hot regions. The maximum change was about 100% for the cold region and 10% for the hot lesion using KEM, against the 37% and 8% obtained with HKEM. The findings of this work suggest that including PET information in the kernel enhances the flexibility of the reconstruction in case of spatial inconsistency. Nevertheless, accurate registration and choice of the appropriate MR image for the creation of the kernel is essential to avoid artifacts, blurring, and bias.

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-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.

Coupled regularization with multiple data discrepancies

We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral or multimodality inverse problems, but also in inverse problems with dynamic data. We consider this setting in a rather general framework and derive stability and convergence results, including convergence rates. In particular, we show how parameter choice strategies adapted to the interplay of different data channels allow to improve upon convergence rates that would be obtained by treating all channels equally. Motivated by concrete applications, our results are obtained under rather general assumptions that allow to include the Kullback-Leibler divergence as data discrepancy term. To simplify their application to concrete settings, we further elaborate several practically relevant special cases in detail. To complement the analytical results, we also provide an algorithmic framework and source code that allows to solve a class of jointly regularized inverse problems with any number of data discrepancies. As concrete applications, we show numerical results for multi-contrast MR and joint MR-PET reconstruction.

Penalized maximum likelihood simultaneous longitudinal PET image reconstruction with difference-image priors

PURPOSE

Many clinical contexts require the acquisition of multiple positron emission tomography (PET) scans of a single subject, for example, to observe and quantitate changes in functional behaviour in tumors after treatment in oncology. Typically, the datasets from each of these scans are reconstructed individually, without exploiting the similarities between them. We have recently shown that sharing information between longitudinal PET datasets by penalizing voxel-wise differences during image reconstruction can improve reconstructed images by reducing background noise and increasing the contrast-to-noise ratio of high-activity lesions. Here, we present two additional novel longitudinal difference-image priors and evaluate their performance using two-dimesional (2D) simulation studies and a three-dimensional (3D) real dataset case study.

METHODS

We have previously proposed a simultaneous difference-image-based penalized maximum likelihood (PML) longitudinal image reconstruction method that encourages sparse difference images (DS-PML), and in this work we propose two further novel prior terms. The priors are designed to encourage longitudinal images with corresponding differences which have (a) low entropy (DE-PML), and (b) high sparsity in their spatial gradients (DTV-PML). These two new priors and the originally proposed longitudinal prior were applied to 2D-simulated treatment response [¹⁸ F]fluorodeoxyglucose (FDG) brain tumor datasets and compared to standard maximum likelihood expectation-maximization (MLEM) reconstructions. These 2D simulation studies explored the effects of penalty strengths, tumor behaviour, and interscan coupling on reconstructed images. Finally, a real two-scan longitudinal data series acquired from a head and neck cancer patient was reconstructed with the proposed methods and the results compared to standard reconstruction methods.

RESULTS

Using any of the three priors with an appropriate penalty strength produced images with noise levels equivalent to those seen when using standard reconstructions with increased counts levels. In tumor regions, each method produces subtly different results in terms of preservation of tumor quantitation and reconstruction root mean-squared error (RMSE). In particular, in the two-scan simulations, the DE-PML method produced tumor means in close agreement with MLEM reconstructions, while the DTV-PML method produced the lowest errors due to noise reduction within the tumor. Across a range of tumor responses and different numbers of scans, similar results were observed, with DTV-PML producing the lowest errors of the three priors and DE-PML producing the lowest bias. Similar improvements were observed in the reconstructions of the real longitudinal datasets, although imperfect alignment of the two PET images resulted in additional changes in the difference image that affected the performance of the proposed methods.

CONCLUSION

Reconstruction of longitudinal datasets by penalizing difference images between pairs of scans from a data series allows for noise reduction in all reconstructed images. An appropriate choice of penalty term and penalty strength allows for this noise reduction to be achieved while maintaining reconstruction performance in regions of change, either in terms of quantitation of mean intensity via DE-PML, or in terms of tumor RMSE via DTV-PML. Overall, improving the image quality of longitudinal datasets via simultaneous reconstruction has the potential to improve upon currently used methods, allow dose reduction, or reduce scan time while maintaining image quality at current levels.

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.

Direct Patlak Reconstruction From Dynamic PET Data Using the Kernel Method With MRI Information Based on Structural Similarity

Positron emission tomography (PET) is a functional imaging modality widely used in oncology, cardiology, and neuroscience. It is highly sensitive, but suffers from relatively poor spatial resolution, as compared with anatomical imaging modalities, such as magnetic resonance imaging (MRI). With the recent development of combined PET/MR systems, we can improve the PET image quality by incorporating MR information into image reconstruction. Previously, kernel learning has been successfully embedded into static and dynamic PET image reconstruction using either PET temporal or MRI information. Here, we combine both PET temporal and MRI information adaptively to improve the quality of direct Patlak reconstruction. We examined different approaches to combine the PET and MRI information in kernel learning to address the issue of potential mismatches between MRI and PET signals. Computer simulations and hybrid real-patient data acquired on a simultaneous PET/MR scanner were used to evaluate the proposed methods. Results show that the method that combines PET temporal information and MRI spatial information adaptively based on the structure similarity index has the best performance in terms of noise reduction and resolution improvement.

Evaluation of Parallel Level Sets and Bowsher's Method as Segmentation-Free Anatomical Priors for Time-of-Flight PET Reconstruction

In this article, we evaluate Parallel Level Sets (PLS) and Bowsher's method as segmentation-free anatomical priors for regularized brain positron emission tomography (PET) reconstruction. We derive the proximity operators for two PLS priors and use the EM-TV algorithm in combination with the first order primal-dual algorithm by Chambolle and Pock to solve the non-smooth optimization problem for PET reconstruction with PLS regularization. In addition, we compare the performance of two PLS versions against the symmetric and asymmetric Bowsher priors with quadratic and relative difference penalty function. For this aim, we first evaluate reconstructions of 30 noise realizations of simulated PET data derived from a real hybrid positron emission tomography/magnetic resonance imaging (PET/MR) acquisition in terms of regional bias and noise. Second, we evaluate reconstructions of a real brain PET/MR data set acquired on a GE Signa time-of-flight PET/MR in a similar way. The reconstructions of simulated and real 3D PET/MR data show that all priors were superior to post-smoothed maximum likelihood expectation maximization with ordered subsets (OSEM) in terms of bias-noise characteristics in different regions of interest where the PET uptake follows anatomical boundaries. Our implementation of the asymmetric Bowsher prior showed slightly superior performance compared with the two versions of PLS and the symmetric Bowsher prior. At very high regularization weights, all investigated anatomical priors suffer from the transfer of non-shared gradients.

NiftyPET: a High-throughput Software Platform for High Quantitative Accuracy and Precision PET Imaging and Analysis

We present a standalone, scalable and high-throughput software platform for PET image reconstruction and analysis. We focus on high fidelity modelling of the acquisition processes to provide high accuracy and precision quantitative imaging, especially for large axial field of view scanners. All the core routines are implemented using parallel computing available from within the Python package NiftyPET, enabling easy access, manipulation and visualisation of data at any processing stage. The pipeline of the platform starts from MR and raw PET input data and is divided into the following processing stages: (1) list-mode data processing; (2) accurate attenuation coefficient map generation; (3) detector normalisation; (4) exact forward and back projection between sinogram and image space; (5) estimation of reduced-variance random events; (6) high accuracy fully 3D estimation of scatter events; (7) voxel-based partial volume correction; (8) region- and voxel-level image analysis. We demonstrate the advantages of this platform using an amyloid brain scan where all the processing is executed from a single and uniform computational environment in Python. The high accuracy acquisition modelling is achieved through span-1 (no axial compression) ray tracing for true, random and scatter events. Furthermore, the platform offers uncertainty estimation of any image derived statistic to facilitate robust tracking of subtle physiological changes in longitudinal studies. The platform also supports the development of new reconstruction and analysis algorithms through restricting the axial field of view to any set of rings covering a region of interest and thus performing fully 3D reconstruction and corrections using real data significantly faster. All the software is available as open source with the accompanying wiki-page and test data.

Simultaneous maximum a posteriori longitudinal PET image reconstruction

Positron emission tomography (PET) is frequently used to monitor functional changes that occur over extended time scales, for example in longitudinal oncology PET protocols that include routine clinical follow-up scans to assess the efficacy of a course of treatment. In these contexts PET datasets are currently reconstructed into images using single-dataset reconstruction methods. Inspired by recently proposed joint PET-MR reconstruction methods, we propose to reconstruct longitudinal datasets simultaneously by using a joint penalty term in order to exploit the high degree of similarity between longitudinal images. We achieved this by penalising voxel-wise differences between pairs of longitudinal PET images in a one-step-late maximum a posteriori (MAP) fashion, resulting in the MAP simultaneous longitudinal reconstruction (SLR) method. The proposed method reduced reconstruction errors and visually improved images relative to standard maximum likelihood expectation-maximisation (ML-EM) in simulated 2D longitudinal brain tumour scans. In reconstructions of split real 3D data with inserted simulated tumours, noise across images reconstructed with MAP-SLR was reduced to levels equivalent to doubling the number of detected counts when using ML-EM. Furthermore, quantification of tumour activities was largely preserved over a variety of longitudinal tumour changes, including changes in size and activity, with larger changes inducing larger biases relative to standard ML-EM reconstructions. Similar improvements were observed for a range of counts levels, demonstrating the robustness of the method when used with a single penalty strength. The results suggest that longitudinal regularisation is a simple but effective method of improving reconstructed PET images without using resolution degrading priors.

PET image reconstruction using multi-parametric anato-functional priors

In this study, we investigate the application of multi-parametric anato-functional (MR-PET) priors for the maximum a posteriori (MAP) reconstruction of brain PET data in order to address the limitations of the conventional anatomical priors in the presence of PET-MR mismatches. In addition to partial volume correction benefits, the suitability of these priors for reconstruction of low-count PET data is also introduced and demonstrated, comparing to standard maximum-likelihood (ML) reconstruction of high-count data. The conventional local Tikhonov and total variation (TV) priors and current state-of-the-art anatomical priors including the Kaipio, non-local Tikhonov prior with Bowsher and Gaussian similarity kernels are investigated and presented in a unified framework. The Gaussian kernels are calculated using both voxel- and patch-based feature vectors. To cope with PET and MR mismatches, the Bowsher and Gaussian priors are extended to multi-parametric priors. In addition, we propose a modified joint Burg entropy prior that by definition exploits all parametric information in the MAP reconstruction of PET data. The performance of the priors was extensively evaluated using 3D simulations and two clinical brain datasets of [18F]florbetaben and [18F]FDG radiotracers. For simulations, several anato-functional mismatches were intentionally introduced between the PET and MR images, and furthermore, for the FDG clinical dataset, two PET-unique active tumours were embedded in the PET data. Our simulation results showed that the joint Burg entropy prior far outperformed the conventional anatomical priors in terms of preserving PET unique lesions, while still reconstructing functional boundaries with corresponding MR boundaries. In addition, the multi-parametric extension of the Gaussian and Bowsher priors led to enhanced preservation of edge and PET unique features and also an improved bias-variance performance. In agreement with the simulation results, the clinical results also showed that the Gaussian prior with voxel-based feature vectors, the Bowsher and the joint Burg entropy priors were the best performing priors. However, for the FDG dataset with simulated tumours, the TV and proposed priors were capable of preserving the PET-unique tumours. Finally, an important outcome was the demonstration that the MAP reconstruction of a low-count FDG PET dataset using the proposed joint entropy prior can lead to comparable image quality to a conventional ML reconstruction with up to 5 times more counts. In conclusion, multi-parametric anato-functional priors provide a solution to address the pitfalls of the conventional priors and are therefore likely to increase the diagnostic confidence in MR-guided PET image reconstructions.