FAWN: Floor-and-Walls Normal Regularization for Direct Neural TSDF Reconstruction

In dynamic PET, direct parametric reconstruction is advantageous over conventional kinetic modeling method in noise reduction. Direct reconstruction with accurate input function has been investigated. However, clinical application of dynamic PET is limited by technical complication in measuring the input function from patient blood samples. Population-based input function (PBIF) is an alternative approach and has been demonstrated to be feasible in regions of interest (ROI) -based kinetic analysis. The objective of this work is to investigate the performance of direct 4D Patlak reconstruction in dynamic FDG PET imaging with PBIF.A direct 4D Patlak reconstruction strategy with PBIF was proposed. A nested technique was used to accelerate the convergence. Dynamic images and unscaled parametric images were generated from direct Patlak reconstruction with unscaled PBIF. The scaling factors estimated from dynamic images were used after the direct reconstruction due to the linear relationship between dynamic images and kinetic parameters. Phantom simulation, preclinical scans and ongoing clinical scans were performed to compare the indirect and direct reconstruction with PBIF. The Ki images generated from direct analysis were less noisy than those generated from indirect analysis. In phantom studies, the directly reconstructed images at convergence shows less noise and comparable bias. For both simulated and experimental data, similar scaled input functions were obtained in the indirect and direct analysis with PBIF. With shorter acquisition time, more iterations are required to reach convergence, while the advantage of direct reconstruction is more remarkable.Our proposed direct reconstruction strategy with PBIF was demonstrated to be feasible. Compared with Ki images generated from indirect analysis, directly reconstructed Ki images showed better performance in terms of less variation and comparable bias.

Abstract. State-of-the art climate prediction systems have recently included a carbon component. While physical-state variables are assimilated in reconstruction simulations, land and ocean biogeochemical state variables adjust to the state acquired through this assimilation indirectly instead of being assimilated themselves. In the absence of comprehensive biogeochemical reanalysis products, such an approach is pragmatic. Here we evaluate a potential advantage of having perfect carbon cycle observational products to be used for direct carbon cycle reconstruction. Within an idealized perfect-model framework, we reconstruct a 50-year target period from a control simulation. We nudge variables from this target onto arbitrary initial conditions, mimicking an assimilation simulation generating initial conditions for hindcast experiments of prediction systems. Interested in the ability to reconstruct global atmospheric CO2, we focus on the global carbon cycle reconstruction performance and predictive skill. We find that indirect carbon cycle reconstruction through physical fields reproduces the target variations. While reproducing the large-scale variations, nudging introduces systematic regional biases in the physical-state variables to which biogeochemical cycles react very sensitively. Initial conditions in the oceanic carbon cycle are sufficiently well reconstructed indirectly. Direct reconstruction slightly improves initial conditions. Indirect reconstruction of global terrestrial carbon cycle initial conditions are also sufficiently well reconstructed by the physics reconstruction alone. Direct reconstruction negligibly improves air–land CO2 flux. Atmospheric CO2 is indirectly very well reconstructed. Direct reconstruction of the marine and terrestrial carbon cycles slightly improves reconstruction while establishing persistent biases. We find improvements in global carbon cycle predictive skill from direct reconstruction compared to indirect reconstruction. After correcting for mean bias, indirect and direct reconstruction both predict the target similarly well and only moderately worse than perfect initialization after the first lead year. Our perfect-model study shows that indirect carbon cycle reconstruction yields satisfying initial conditions for global CO2 flux and atmospheric CO2. Direct carbon cycle reconstruction adds little improvement to the global carbon cycle because imperfect reconstruction of the physical climate state impedes better biogeochemical reconstruction. These minor improvements in initial conditions yield little improvement in initialized perfect-model predictive skill. We label these minor improvements due to direct carbon cycle reconstruction “trivial”, as mean bias reduction yields similar improvements. As reconstruction biases in real-world prediction systems are likely stronger, our results add confidence to the current practice of indirect reconstruction in carbon cycle prediction systems.

A personal experience with direct reconstruction and extra-anatomic bypass for aortoiliofemoral occlusive disease

Cardiac perfusion PET data can be reconstructed as a dynamic sequence and kinetic modeling performed to quantify myocardial blood flow, or reconstructed as static gated images to quantify function. Parametric images from dynamic PET are conventionally not gated, to allow use of all events with lower noise. An alternative method for dynamic PET is to incorporate the kinetic model into the reconstruction algorithm itself, bypassing the generation of a time series of emission images and directly producing parametric images. So-called "direct reconstruction" can produce parametric images with lower noise than the conventional method because the noise distribution is more easily modeled in projection space than in image space. In this work, we develop direct reconstruction of cardiac-gated parametric images for 82 Rb PET with an extension of the Parametric Motion compensation OSEM List mode Algorithm for Resolution-recovery reconstruction for the one tissue model (PMOLAR-1T). PMOLAR-1T was extended to accommodate model terms to account for spillover from the left and right ventricles into the myocardium. The algorithm was evaluated on a 4D simulated 82 Rb dataset, including a perfusion defect, as well as a human 82 Rb list mode acquisition. The simulated list mode was subsampled into replicates, each with counts comparable to one gate of a gated acquisition. Parametric images were produced by the indirect (separate reconstructions and modeling) and direct methods for each of eight low-count and eight normal-count replicates of the simulated data, and each of eight cardiac gates for the human data. For the direct method, two initialization schemes were tested: uniform initialization, and initialization with the filtered iteration 1 result of the indirect method. For the human dataset, event-by-event respiratory motion compensation was included. The indirect and direct methods were compared for the simulated dataset in terms of bias and coefficient of variation as a function of iteration. Convergence of direct reconstruction was slow with uniform initialization; lower bias was achieved in fewer iterations by initializing with the filtered indirect iteration 1 images. For most parameters and regions evaluated, the direct method achieved the same or lower absolute bias at matched iteration as the indirect method, with 23%-65% lower noise. Additionally, the direct method gave better contrast between the perfusion defect and surrounding normal tissue than the indirect method. Gated parametric images from the human dataset had comparable relative performance of indirect and direct, in terms of mean parameter values per iteration. Changes in myocardial wall thickness and blood pool size across gates were readily visible in the gated parametric images, with higher contrast between myocardium and left ventricle blood pool in parametric images than gated SUV images. Direct reconstruction can produce parametric images with less noise than the indirect method, opening the potential utility of gated parametric imaging for perfusion PET.

The world's first 194-cm-long total-body PET/CT scanner (uEXPLORER) has been built by the EXPLORER Consortium to offer a transformative platform for human molecular imaging in clinical research and health care. Its total-body coverage and ultra-high sensitivity provide opportunities for more accurate tracer kinetic analysis in studies of physiology, biochemistry, and pharmacology. The objective of this study was to demonstrate the capability of total-body parametric imaging and to quantify the improvement in image quality and kinetic parameter estimation by direct and kernel reconstruction of the uEXPLORER data. Methods: We developed quantitative parametric image reconstruction methods for kinetic analysis and used them to analyze the first human dynamic total-body PET study. A healthy female subject was recruited, and a 1-h dynamic scan was acquired during and after an intravenous injection of 256 MBq of 18F-FDG. Dynamic data were reconstructed using a 3-dimensional time-of-flight list-mode ordered-subsets expectation maximization (OSEM) algorithm and a kernel-based algorithm with all quantitative corrections implemented in the forward model. The Patlak graphical model was used to analyze the 18F-FDG kinetics in the whole body. The input function was extracted from a region over the descending aorta. For comparison, indirect Patlak analysis from reconstructed frames and direct reconstruction of parametric images from the list-mode data were obtained for the last 30 min of data. Results: Images reconstructed by OSEM showed good quality with low noise, even for the 1-s frames. The image quality was further improved using the kernel method. Total-body Patlak parametric images were obtained using either indirect estimation or direct reconstruction. The direct reconstruction method improved the parametric image quality, having a better contrast-versus-noise tradeoff than the indirect method, with a 2- to 3-fold variance reduction. The kernel-based indirect Patlak method offered image quality similar to the direct Patlak method, with less computation time and faster convergence. Conclusion: This study demonstrated the capability of total-body parametric imaging using the uEXPLORER. Furthermore, the results showed the benefits of kernel-regularized reconstruction and direct parametric reconstruction. Both can achieve superior image quality for tracer kinetic studies compared with the conventional indirect OSEM for total-body imaging.

In myocardial perfusion imaging with dynamic positron emission tomography (PET), direct parametric reconstruction from the projection data allows accurate modeling of the Poisson noise in the projection domain to provide more reliable estimate of the parametric images. In this study, we propose to incorporate a superior denoiser to efficiently suppress the unfavorable noise propagation during the direct reconstruction. The dictionary learning (DL) based sparse representation serves as a regularization term to constrain the intermediate K1 estimation. We rewrite the DL regularizer into a voxel-separable form to facilitate the decoupling of a DL penalized curve fitting from the reconstruction of dynamic frames. The nonlinear fitting is then solved by a damped Newton method with uniform initialization. Using simulated and patient 82Rb dynamic PET data, we study the performance of the proposed DL direct algorithm and quantitatively compare it with the indirect method with or without post-filtering, the direct reconstruction without regularization, and the quadratic penalty regularized direct algorithm. The DL regularized direct reconstruction achieves improved noise versus bias performance in the reconstructed K1 images as well as superior recovery of a reduced myocardial blood flow defect. The dictionary learned from a 3D self-created hollow sphere image yields comparable results to those using the dictionary learned from the corresponding magnetic resonance image. The uniform initializations converge to K1 estimations similar to the result from initializing with the indirect reconstruction. To summarize, we demonstrate the potential of the proposed DL constrained direct parametric reconstruction in improving quantitative dynamic PET imaging.

Direct reconstruction methods have been developed to estimate parametric images directly from the measured sinogram by combining the PET imaging model and tracer kinetics in an integrated framework. Due to limited counts received, especially for low-dose scenarios, SNR and resolution of parametric images produced by direct reconstruction frameworks are still limited. Recently supervised deep learning methods have been successfully applied to medical imaging denoising/reconstruction when large number of high-quality training labels are available. For static PET imaging, high-quality training labels can be acquired by extending scanning time. However, this is not feasible for dynamic PET imaging, where the scanning time is already long enough. In this work, we present a novel unsupervised deep learning method for direct Patlak reconstruction from low-dose dynamic PET. The training label is measured sinogram itself and the only requirement is the patients own anatomical prior image, which is readily available from PET/CT or PET/MR scans. Experiment evaluation based on a low-dose dynamic dataset shows that the proposed method can outperform Gaussian post-smoothing and anatomically-guided direct reconstruction using the kernel method.

Estimation of nonlinear micro-parameters is a computationally demanding and fairly challenging process, since it involves the use of rather slow iterative nonlinear fitting algorithms and it often results in very noisy voxel-wise parametric maps. Direct reconstruction algorithms can provide parametric maps with reduced variance, but usually the overall reconstruction is impractically time consuming with common nonlinear fitting algorithms. In this work we employed a recently proposed direct parametric image reconstruction algorithm to estimate the parametric maps of all micro-parameters of a two-tissue compartment model, used to describe the kinetics of [[Formula: see text]F]FDG. The algorithm decouples the tomographic and the kinetic modelling problems, allowing the use of previously developed post-reconstruction methods, such as the generalised linear least squares (GLLS) algorithm. Results on both clinical and simulated data showed that the proposed direct reconstruction method provides considerable quantitative and qualitative improvements for all micro-parameters compared to the conventional post-reconstruction fitting method. Additionally, region-wise comparison of all parametric maps against the well-established filtered back projection followed by post-reconstruction non-linear fitting, as well as the direct Patlak method, showed substantial quantitative agreement in all regions. The proposed direct parametric reconstruction algorithm is a promising approach towards the estimation of all individual microparameters of any compartment model. In addition, due to the linearised nature of the GLLS algorithm, the fitting step can be very efficiently implemented and, therefore, it does not considerably affect the overall reconstruction time.

Postprocessing offers the possibility of real-time creation of thickened slabs from a set of thin slices. This allows the interactive change from thick to thin slices for better evaluation of unclear lesions. As a result the clinical workflow of MSCT evaluation can be improved. However, to be able to apply this postprocessing software in the clinical routine, degradations in the image quality (compared to standard original reconstructed images) have to be avoided. The purpose of this study was to compare the image quality of thickened slabs from MSCT chest examinations that have either been directly reconstructed from the raw data or have been retrospectively generated via postprocessing. Chest MSCT examinations of 20 patients (mean age: 56 years) were performed on a 16-slice MSCT scanner (Mx8000IDT16, Philips, Best, Netherlands) using the following scan parameters: 120 kV, 94 effective mAs, 16 x 1.5 mm collimation, 512 x 512 matrix, field of view 371 x 371 mm, CTDIvol = 6.3 mGy, DLP = 210 mGyxcm). Slices with a thickness of 3 and 5 mm were generated for each examination both directly from the raw data and via postprocessing. Corresponding images from postprocessing and direct reconstruction (lung/soft tissue window) were evaluated by two radiologists with respect to 5 criteria on the basis of a five-point scale: organ structure, contour of small objects, contrast, image noise and artifacts. Differences between both data sets regarding image quality were assessed for each of the 5 criteria using a Wilcoxon test with Bonferroni correction. In addition, image noise was analyzed quantitatively in a region of interest in the aorta. For the lung and soft tissue window, both reviewers and all criteria, no differences in image quality were detected between the thickened slices obtained via direct reconstruction and the postprocessing method. In 96 % and 95 % of the cases images of the two reconstruction methods were graded identically for 3 mm and 5 mm slices. In the remaining 4 % and 5 %, the evaluations differed only by one point on the five-point scale. The median grade of the first reviewer was 1 and that of the second reviewer was 2. There were no differences in the quantitative analysis of image noise between both methods. The interactive creation of thickened slices is an effective tool for the evaluation of MSCT examinations. For the defined scan parameters in this study there were no differences in image quality between postprocessing methods (e. g. slab viewer) and direct image reconstruction.

Patlak model is widely used in 18F-FDG dynamic positron emission tomography (PET) imaging, where the estimated parametric images reveal important biochemical and physiology information. Because of better noise modeling and more information extracted from raw sinogram, direct Patlak reconstruction gains its popularity over the indirect approach which utilizes reconstructed dynamic PET images alone. As the prerequisite of direct Patlak methods, raw data from dynamic PET are rarely stored in clinics and difficult to obtain. In addition, the direct reconstruction is time-consuming due to the bottleneck of multiple-frame reconstruction. All of these impede the clinical adoption of direct Patlak reconstruction. In this work, we proposed a data-driven framework which maps the dynamic PET images to the high-quality motion-corrected direct Patlak images through a convolutional neural network. For the patient’s motion during the long period of dynamic PET scan, we combined the correction with the backward/forward projection in direct reconstruction to better fit the statistical model. Results based on fifteen clinical 18F-FDG dynamic brain PET datasets demonstrates the superiority of the proposed framework over Gaussian, nonlocal mean and BM4D denoising, regarding the image bias and contrast-to-noise ratio.

Direct parametric image reconstruction has the potential to reduce variance in parameter estimates when applied to PET/CT data. One complication when estimating parametric maps in the body is the difficulty of finding one single model to describe all the different kinetics in the field of view (FOV). Contrary to the post-reconstruction kinetic analysis though, any errors (bias) from the discrepancy between the model and the observed kinetics in the direct 4D reconstruction can potentially propagate spatially from unimportant areas to areas of interest. In this work we investigate this effect on simulated 4-D datasets based on a digital body phantom. Different realistic cases were simulated including differential input functions in the FOV and organs with different kinetics. Micro-parameters (K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,Vd, bv) where estimated using a newly proposed spatiotemporal 4D image reconstruction algorithm as well as using post-reconstruction kinetic analysis on noiseless and noisy datasets simulating [ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15</sup> O] H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O kinetics in the body. Bias analysis both in noiseless and noisy data showed a bias from badly modelled areas spatially propagates to other regions of interest in the direct reconstruction. Critically though under noisy conditions even with the bias propagation, the direct reconstruction method still outperforms the conventional post-reconstruction methodology. Nevertheless there is a need to ensure that appropriate models are chosen to describe the kinetics in the entire FOV with approaches such as data-driven adaptive kinetic modelling worth exploring.

Dynamic fluorescence molecular tomography (FMT) has the potential to quantify physiological or biochemical information, known as pharmacokinetic parameters, which are important for cancer detection, drug development and delivery etc. To image those parameters, there are indirect methods, which are easier to implement but tend to provide images with low signal-to-noise ratio, and direct methods, which model all the measurement noises together and are statistically more efficient. The direct reconstruction methods in dynamic FMT have attracted a lot of attention recently. However, the coupling of tomographic image reconstruction and nonlinearity of kinetic parameter estimation due to the compartment modeling has imposed a huge computational burden to the direct reconstruction of the kinetic parameters. In this paper, we propose to take advantage of both the direct and indirect reconstruction ideas through a variable splitting strategy under the augmented Lagrangian framework. Each iteration of the direct reconstruction is split into two steps: the dynamic FMT image reconstruction and the node-wise nonlinear least squares fitting of the pharmacokinetic parameter images. Through numerical simulation studies, we have found that the proposed algorithm can achieve good reconstruction results within a small amount of time. This will be the first step for a combined dynamic PET and FMT imaging in the future.

Deep learning is an emerging reconstruction method for positron emission tomography (PET), which can tackle complex PET corrections in an integrated procedure. This paper optimizes the direct PET reconstruction from sinogram on a long axial field of view (LAFOV) PET. This paper proposes a novel deep learning architecture to reduce the biases during direct reconstruction from sinograms to images. This architecture is based on an encoder-decoder network, where the perceptual loss is used with pre-trained convolutional layers. It is trained and tested on data of 80 patients acquired from recent Siemens Biograph Vision Quadra long axial FOV (LAFOV) PET/CT. The patients are randomly split into a training dataset of 60 patients, a validation dataset of 10 patients, and a test dataset of 10 patients. The 3D sinograms are converted into 2D sinogram slices and used as input to the network. In addition, the vendor reconstructed images are considered as ground truths. Finally, the proposed method is compared with DeepPET, a benchmark deep learning method for PET reconstruction. Compared with DeepPET, the proposed network significantly reduces the root-mean-squared error (NRMSE) from 0.63 to 0.6 (p &lt; 0.01) and increases the structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) from 0.93 to 0.95 (p &lt; 0.01) and from 82.02 to 82.36 (p &lt; 0.01), respectively. The reconstruction time is approximately 10s per patient, which is shortened by 23 times compared with the conventional method. The errors of mean standardized uptake values (SUVmean) for lesions between ground truth and the predicted result are reduced from 33.5 to 18.7% (p = 0.03). In addition, the error of max SUV is reduced from 32.7 to 21.8% (p = 0.02). The results demonstrate the feasibility of using deep learning to reconstruct images with acceptable image quality and short reconstruction time. It is shown that the proposed method can improve the quality of deep learning-based reconstructed images without additional CT images for attenuation and scattering corrections. This study demonstrated the feasibility of deep learning to rapidly reconstruct images without additional CT images for complex corrections from actual clinical measurements on LAFOV PET. Despite improving the current development, AI-based reconstruction does not work appropriately for untrained scenarios due to limited extrapolation capability and cannot completely replace conventional reconstruction currently.

Dynamic PET myocardial perfusion imaging (MPI) used in conjunction with tracer kinetic modeling enables the quantification of absolute myocardial blood flow (MBF). However, MBF maps computed using the traditional indirect method (i.e. post-reconstruction voxel-wise fitting of kinetic model to PET time-activity-curves-TACs) suffer from poor signal-to-noise ratio (SNR). Direct reconstruction of kinetic parameters from raw PET projection data has been shown to offer parametric images with higher SNR compared to the indirect method. The aim of this study was to extend and evaluate the performance of a direct parametric reconstruction method using in vivo dynamic PET MPI data for the purpose of quantifying MBF. Dynamic PET MPI studies were performed on two healthy pigs using a Siemens Biograph mMR scanner. List-mode PET data for each animal were acquired following a bolus injection of ~7–8 mCi of 18F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Additionally, eight independent noise realizations of both scans—each containing 1/8th of the total number of events—were generated from the original list-mode data. Dynamic sinograms were then used to compute parametric maps using the conventional indirect method and the proposed direct method. For both methods, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of 18F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using two fully-3D reconstruction techniques: the standard ordered subset expectation maximization (OSEM) reconstruction algorithm on one side, and the one-step late maximum a posteriori (OSL-MAP) algorithm on the other side, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel- and segment-wise estimates of , the tracer transport rate (ml · min−1 · ml−1), to those obtained using the indirect method applied to both OSEM and OSL-MAP dynamic reconstructions. The proposed direct reconstruction method produced maps with visibly lower noise than the indirect method based on OSEM and OSL-MAP reconstructions. At normal count levels, the direct method was shown to outperform the indirect method based on OSL-MAP in the sense that at matched level of bias, reduced regional noise levels were obtained. At lower count levels, the direct method produced estimates with significantly lower standard deviation across noise realizations than the indirect method based on OSL-MAP at matched bias level. In all cases, the direct method yielded lower noise and standard deviation than the indirect method based on OSEM. Overall, the proposed direct reconstruction offered a better bias-variance tradeoff than the indirect method applied to either OSEM and OSL-MAP. Direct parametric reconstruction as applied to in vivo dynamic PET MPI data is therefore a promising method for producing MBF maps with lower variance.

Due to limited counts in voxel-wise time activity curves, the indirect methods that generate kinetic parametric image from dynamic PET reconstructions often have poor image quality. The TOF PET data can be naturally and efficiently stored in histoimage, and 4D tracer distribution can be efficiently reconstructed using the DIRECT (Direct Image REConstruction for Tof) approaches. We aim to develop efficient dynamic/parametric reconstruction with improved quantitative quality from time-of-flight PET data by taking advantage of its intrinsic kinetic models in our DIRECT frameworks. We have implemented volume of interest (VOI) based and voxel-wise parametric fitting using the linearized Patlak model. We further modified DIRECT reconstructions to support 4D nested reconstruction approach with interleaving tomographic reconstruction and parametric fitting at each iteration. To evaluate proposed dynamic reconstruction approaches, we generate 4D dynamic data sets using the synthetic lesion embedding technique. First, a human subject injected with FDG was scanned on the PennPET Explorer scanner configured with 70 cm axial FOV. Then lung and liver lesions were synthetically embedded using pre-scanned sphere data sets with predetermined time-activity curves. We showed that VOI based method can accurately estimate the Patlak parameters from the frame based reconstructions after corrections. The 4D nested DIRECT reconstruction with Patlak fitting can substantially reduce noise in the reconstructed image frames and provide efficient and feasible tool for direct reconstruction of kinetic parametric image.