Scatter Estimation Research Articles

Deep learning-based 3D in vivo dose reconstruction with an electronic portal imaging device for magnetic resonance-linear accelerators: a proof of concept study

Objective. To develop a novel deep learning-based 3D in vivo dose reconstruction framework with an electronic portal imaging device (EPID) for magnetic resonance-linear accelerators (MR-LINACs). Approach. The proposed method directly back-projected 2D portal dose into 3D patient coarse dose, which bypassed the complicated patient-to-EPID scatter estimation step used in conventional methods. A pre-trained convolutional neural network (CNN) was then employed to map the coarse dose to the final accurate dose. The electron return effect caused by the magnetic field was captured with the CNN model. Patient dose and portal dose datasets were synchronously generated with Monte Carlo simulation for 96 patients (78 cases for training and validation and 18 cases for testing) treated with fixed-beam intensity-modulated radiotherapy in four different tumor sites, including the brain, nasopharynx, lung, and rectum. Beam angles from the training dataset were further rotated 2–3 times, and doses were recalculated to augment the datasets. Results. The comparison between reconstructed doses and MC ground truth doses showed mean absolute errors <0.88% for all tumor sites. The averaged 3D γ-passing rates (3%, 2 mm) were 97.42%±2.66% (brain), 98.53%±0.95% (nasopharynx), 99.41%±0.46% (lung), and 98.63%±1.01% (rectum). The dose volume histograms and indices also showed good consistency. The average dose reconstruction time, including back projection and CNN dose mapping, was less than 3 s for each individual beam. Significance. The proposed method can be potentially used for accurate and fast 3D dosimetric verification for online adaptive radiotherapy using MR-LINACs.

Finite element analysis of fracture behavior in ceramics: Prediction of strength distribution using microstructural features

AbstractThe estimation of the strength scatter caused by internal defects is necessary in analyzing a reliable design of advanced ceramic components. In this study, we proposed a finite element analysis methodology to predict the stochastic fracture behavior of ceramics based on the microstructural features obtained by the scanning electron microscopy and X‐ray computed tomography. Here, the two‐ and three‐dimensional distribution microstructural data are approximated by various probability density functions and are reflected in the dispersion of parameters of the damage model via a fracture mechanics model. We then applied the proposed method to alumina fine ceramics sintered at three different temperatures, and performed the three‐point bending test. Furthermore, the numerically created Weibull distributions were compared with those obtained experimentally. Our analysis results confirm that the proposed method can reasonably predict the strength scatter in ceramics.

Planning CT-guided robust and fast cone-beam CT scatter correction using a local filtration technique.

Cone-beam CT (CBCT) has been widely utilized in image-guided radiotherapy. Planning CT (pCT)-aided CBCT scatter correction could further enhance image quality and extend CBCT application to dose calculation and adaptive planning. Nevertheless, existing pCT-based approaches demand accurate registration between pCT and CBCT, leading to limited imaging performance and increased computational cost when large anatomical discrepancies exist. In this work, we proposed a robust and fast CBCT scatter correction method using local filtration technique and rigid registration between pCT and CBCT (LF-RR). First of all, the pCT was rigidly registered with CBCT, then forward projection was performed on registered pCT to create scatter-free projections. The raw scatter signals were obtained via subtracting the scatter-free projections from the measured CBCT projections. Based on frequency and intensity threshold criteria, reliable scatter signals were selected from the raw scatter signals, and further filtered for global scatter estimation via local filtration technique. Finally, corrected CBCT was reconstructed with the projections generated by subtracting the scatter estimation from the raw CBCT projections using FDK algorithm. The LF-RR method was evaluated via comparison with another pCT-based scatter correction method based on Median and Gaussian filters (MG method). Proposed method was first validated on an anthropomorphic pelvis phantom, and showed satisfied performance on scatter removal even when anatomical mismatches were intentionally created on pCT. The quantitative analysis was further performed on four clinical CBCT images. Compared with the uncorrected CBCT, CBCT corrected by MG with rigid registration (MG-RR), MG with deformable registration (MG-DR), and LF-RR reduced the CT number error from to , and HU for adipose and from to , , 3 HU for muscle, respectively. After correction, the spatial non-uniformity (SNU) of CBCT corrected with MG-RR, MG-DR and LF-RR was , , and HU for adipose, and , , and HU for muscle, respectively. Meanwhile, the contrast-to-noise ratio (CNR) between muscle and adipose was increased by a factor of 2.70, 2.89 and 2.56, respectively. Using the LF-RR method, the scatter correction of 656 projections can be finished within 10 s and the corrected volumetric images (200 slices) can be obtained within 2 min. We developed a fast and robust pCT-based CBCT scatter correction method which exploits the local-filtration technique to promote the accuracy of scatter estimation and is resistant to pCT-to-CBCT registration uncertainties. Both phantom and patient studies showed the superiority of the proposed correction in imaging accuracy and computational efficiency, indicating promisingfuture clinical application.

Performance optimization of a tri-hybrid method for estimation of patient scatter into the EPID.

On‐treatment EPID images are contaminated with patient‐generated scattered photons. If this component can be accurately estimated, its effect can be removed, and therefore a corresponding in vivo patient dose estimate will be more accurate. Our group previously developed a "tri‐hybrid" (TH) algorithm to provide fast but accurate estimates of patient‐generated photon scatter. The algorithm uses an analytical method to solve for singly‐scattered photon fluence, a modified Monte Carlo hybrid method to solve for multiply‐scattered photon fluence, and a pencil beam scatter kernel method to solve for electron interaction generated scattered photon fluence. However, for efficient clinical implementation, spatial and energy sampling must be optimized for speed while maintaining overall accuracy.In this work, the most significant sampling issues were examined, including spatial sampling settings for the patient voxel size, the number of Monte Carlo histories used in the modified hybrid MC method, scatter order sampling for the hybrid method, and also a range of energy spectrum sampling (i.e., energy bin sizes).The total predicted patient‐scattered photon fluence entering the EPID was compared with full MC simulation (EGSnrc) for validation. Three phantoms were tested with 6 and 18 MV beam energies, field sizes of 4 × 4, 10 × 10, and 20 × 20 cm2, and source‐to‐imager distance of 140 cm to develop a set of optimal sampling settings.With the recommended sampling, accuracy and precision of the total‐scattered energy fluence of the TH patient scatter prediction method are within 0.9% and 1.2%, respectively, for all test cases compared with full MC simulation results. For the mean energy spectrum across the imaging plane, comparison of TH with full MC simulation showed 95% overlap.This study has optimized sampling settings so that they have minimal impact on patient scatter prediction accuracy while maintaining maximum execution speed, a critical step for future clinical implementation.

Slot-scan dual-energy bone densitometry using motorized X-ray systems.

We investigate the feasibility of slot-scan dual-energy (DE) bone densitometry on motorized radiographic equipment. This approach will enable fast quantitative measurements of areal bone mineral density (aBMD) for opportunistic evaluation of osteoporosis. We investigated DE slot-scan protocols to obtain aBMD measurements at the lumbar spine (L-spine) and hip using a motorized x-ray platform capable of synchronized translation of the x-ray source and flat-panel detector (FPD). The slot dimension was 5 × 20 cm2 . The DE slot views were processed as follows: (1) convolution kernel-based scatter correction, (2) unfiltered backprojection to tile the slots into long-length radiographs, and (3) projection-domain DE decomposition, consisting of an initial adipose-water decomposition in a bone-free region followed by water-CaHA decomposition with adjustment for adipose content. The accuracy and reproducibility of slot-scan aBMD measurements were investigated using a high-fidelity simulator of a robotic x-ray system (Siemens Multitom Rax) in a total of 48 body phantom realizations: four average bone density settings (cortical bone mass fraction: 10-40%), four body sizes (waist circumference, WC=70-106cm), and three lateral shifts of the body within the slot field of view (FOV) (centered and ±1cm off-center). Experimental validations included: (1) x-ray test-bench feasibility study of adipose-water decomposition and (2) initial demonstration of slot-scan DE bone densitometry on the robotic x-ray system using the European Spine Phantom (ESP) with added attenuation (polymethyl methacrylate [PMMA] slabs) ranging 2 to 6cm thick. For the L-spine, the mean aBMD error across all WC settings ranged from 0.08g/cm2 for phantoms with average cortical bone fraction wcortical =10% to ∼0.01g/cm2 for phantoms with wcortical =40%. The L-spine aBMD measurements were fairly robust to changes in body size and positioning, e.g., coefficient of variation (CV) for L1 with wcortical =30% was ∼0.034 for various WC and ∼0.02 for an obese patient (WC=106cm) changing lateral shift. For the hip, the mean aBMD error across all phantom configurations was about 0.07g/cm2 for a centered patient. The reproducibility of hip aBMD was slightly worse than in the L-spine (e.g., in the femoral neck, the CV with respect to changing WC was ∼0.13 for phantom realizations with wcortical =30%) due to more challenging scatter estimation in the presence of an air-tissue interface within the slot FOV. The aBMD of the hip was therefore sensitive to lateral positioning of the patient, especially for obese patients: e.g., the CV with respect to patient lateral shift for femoral neck with WC=106cm and wcortical =30% was 0.14. Empirical evaluations confirmed substantial reduction in aBMD errors with the proposed adipose estimation procedure and demonstrated robust aBMD measurements on the robotic x-ray system, with aBMD errors of ∼0.1g/cm2 across all three simulated ESP vertebrae and all added PMMA attenuator settings. We demonstrated that accurate aBMD measurements can be obtained on a motorized FPD-based x-ray system using DE slot-scans with kernel-based scatter correction, backprojection-based slot view tiling, and DE decomposition with adipose correction.

A robust Hotelling test statistic for one sample case in high dimensional data

The Hotelling statistic is used to test the hypothesis about the location parameter of multivariate Gaussian distribution, and it is significantly sensitive to outliers. Also, we cannot calculate it when the sample size is less than the number of variables because this statistic needs the inverse of the covariance matrix, and the sample covariance matrix is singular in high dimensional data. Although a new approach, based on shrinkage estimation, was proposed to solve this singularity problem, this estimator is still sensitive to outliers. On the other hand, a robust one sample Hotelling statistic was proposed by using the minimum covariance determinant (MCD) estimates instead of classical ones. Since the MCD estimates cannot be calculated when this statistic cannot be used in high-dimensional data. This study proposes to use the minimum regularized covariance determinant (MRCD) estimator instead of classical or MCD. The MRCD estimator is a robust location and scatter estimator, which can be calculated in high-dimensional data. We obtain the asymptotic distribution of the proposed test statistic using Monte Carlo simulations and examine the power and robustness properties of the test statistic with simulated datasets. As a result, we show that the approximate distribution of the test statistic is proper, and the proposed robust test statistic can be used to test the hypothesis about the location parameter of contaminated high dimensional data. Finally, we construct an R function in the MVTests package to perform our proposed test statistic.

Local models for scatter estimation and descattering in polyenergetic X-ray tomography.

We propose a new modeling approach for scatter estimation and descattering in polyenergetic X-ray computed tomography (CT) based on fitting models to local neighborhoods of a training set. X-ray CT is widely used in medical and industrial applications. X-ray scatter, if not accounted for during reconstruction, creates a loss of contrast in CT reconstructions and introduces severe artifacts including cupping, shading, and streaks. Even when these qualitative artifacts are not apparent, scatter can pose a major obstacle in obtaining quantitatively accurate reconstructions. Our approach to estimating scatter is, first, to generate a training set of 2D radiographs with and without scatter using particle transport simulation software. To estimate scatter for a new radiograph, we adaptively fit a scatter model to a small subset of the training data containing the radiographs most similar to it. We compared local and global (fit on full data sets) versions of several X-ray scatter models, including two from the recent literature, as well as a recent deep learning-based scatter model, in the context of descattering and quantitative density reconstruction of simulated, spherically symmetrical, single-material objects comprising shells of various densities. Our results show that, when applied locally, even simple models provide state-of-the-art descattering, reducing the error in density reconstruction due to scatter by more than half.

Deep learning-based forward and cross-scatter correction in dual-source CT.

Dual-source computed tomography (DSCT) uses two source-detector pairs offset by about 90°. In addition to the well-known forward scatter, a special issue in DSCT is cross-scattered radiation from X-ray tube A detected in the detector of system B and vice versa. This effect can lead to artifacts and reduction of the contrast-to-noise ratio of the images. The purpose of this work is to present and evaluate different deep learning-based methods for scatter correction in DSCT. We present different neural network-based methods for forward and cross-scatter correction in DSCT. These deep scatter estimation (DSE) methods mainly differ in the input and output information that is provided for training and inference and in whether they operate on two-dimensional (2D) or on three-dimensional (3D) data. The networks are trained and validated with scatter distributions obtained by our in-house Monte Carlo simulation. The simulated geometry is adapted to a realistic clinical setup. All DSE approaches reduce scatter-induced artifacts and lead to superior results than the measurement-based scatter correction. Forward scatter, under the presence of cross-scatter, is best estimated either by our network that uses the current projection and a couple of neighboring views (fDSE 2D few views) or by our 3D network that processes all projections simultaneously (fDSE 3D). Cross-scatter, under the presence of forward scatter, is best estimated using xSSE XDSE 2D, with xSSE referring to a quick single scatter estimate of cross scatter, or by xDSE 3D that uses all projections simultaneously. By using our proposed networks, the total scatter error in dual could be reduced from about 18HU to approximately 3HU. Deep learning-based scatter correction can reduce scatter artifacts in DSCT. To achieve more accurate cross-scatter estimations, the use of a cross-scatter approximation improves the results. Also, the ability to leverage across different projection angles improves the precision of the algorithm.

Model-Based Learning Network for 3-D Localization in mmWave Communications

Millimeter-wave (mmWave) cloud radio access networks (CRANs) provide new opportunities for accurate cooperative localization, in which large bandwidths and antenna arrays and increased densities of base stations enhance the delay and angular resolution. This study considers the joint location and velocity estimation of user equipment (UE) and scatterers in a three-dimensional mmWave CRAN architecture. Several existing works have achieved satisfactory results by using neural networks (NNs) for localization. However, the black box NN localization method has limited robustness and accuracy and relies on a prohibitive amount of training data to increase localization accuracy. Thus, we propose a model-based learning network for localization to address these problems. In comparison with the black box NN, we combine NNs with geometric models. Specifically, we first develop an unbiased weighted least squares (WLS) estimator by utilizing hybrid delay and angular measurements, which determine the location and velocity of the UE in only one estimator, and can obtain the location and velocity of scatterers further. The proposed estimator can achieve the Cramér-Rao lower bound under small measurement noise and outperforms other state-of-the-art methods. Second, we establish a NN-assisted localization method called NN-WLS by replacing the linear approximations in the proposed WLS localization model with NNs to learn the higher-order error components, thereby enhancing the performance of the estimator, especially in a large noise environment. The solution possesses the powerful learning ability of the NN and the robustness of the proposed geometric model. Moreover, the ensemble learning is applied to improve the localization accuracy further. Comprehensive simulations show that the proposed NN-WLS is superior to the benchmark methods in terms of localization accuracy, robustness, and required time resources.

Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions

The joint estimation of the location vector and the shape matrix of a set of independent and identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both the theoretical and computational viewpoints. This joint estimation problem is framed in the original context of semiparametric models allowing us to handle the (generally unknown) density generator as an infinite-dimensional nuisance parameter. In the first part of the paper, a computationally efficient and memory saving implementation of the robust and semiparmaetric efficient R-estimator for shape matrices is derived. Building upon this result, in the second part, a joint estimator, relying on the Tyler’s M-estimator of location and on the R-estimator of shape matrix, is proposed and its Mean Squared Error (MSE) performance compared with the Semiparametric Cramér-Rao Bound (SCRB).

Assessment of deep learning-based PET attenuation correction frameworks in the sinogram domain

This study set out to investigate various deep learning frameworks for PET attenuation correction in the sinogram domain. Different models for both time-of-flight (TOF) and non-TOF PET emission data were implemented, including direct estimation of the attenuation corrected (AC) emission sinograms from the nonAC sinograms, estimation of the attenuation correction factors (ACFs) from PET emission data, correction of scattered photons prior to training of the models, and separate training of the models for each segment of the emission sinograms. A segmentation-based 2-class AC map was included as a bottom-line technique for comparison of the different models considering PET/CT AC as reference. Fifty clinical TOF PET/CT brain scans were employed for training whereas 20 were used for evaluation of the models. Quantitative analysis of the resulting PET images was carried out through region-wise standardized uptake value (SUV) bias calculation. The models relying on TOF information significantly outperformed the nonTOF models as well as the segmentation-based AC map resulting in maximum SUV bias of 6.5%, 9.5%, and 14.0%, respectively. Estimation of ACFs from either TOF or nonTOF PET emission data was very sensitive to prior scatter correction. However, direct estimation of AC sinograms from nonAC sinograms revealed no sensitivity to scatter correction, thus obviating the need for prior scatter estimation. For TOF PET data, though direct prediction of the AC sinograms does not require prior estimation of scattered photons, it requires input/output channels equal to the number of TOF bins which might be computationally or memory-wise expensive. Prediction of the ACF matrices from TOF emission data is less demanding in terms of memory as it requires only a single channel for output. AC in the sinogram domain of TOF PET data exhibited superior performance compared to both nonTOF and segmentation-based methods. However, such models require multiple input/output channels.

A convolutional neural network for Y90 SPECT/CT scatter estimation

Monte Carlo-based scatter modeling in SPECT has demonstrated the ability on improving image quality and quantitative accuracy but high computational cost. In this study, we describe a deep learning method based on a convolutional neural network (CNN) to increase the image quality, decrease the computation time for SPECT/CT reconstruction. Monte Carlo (MC) simulation and true scatter data are used for training and validation phase and the CNN network is trained to match the MC scatter estimation. In the testing step with a liver subject, visual image quality by CNN was better than MC scatter estimation method. Besides, the CNN scatter estimate was generated over a much shorter period of time than MC model (about 15 seconds for CNN vs ~2 hours for MC). The short processing time with CNN while maintaining quality has high clinical significance for quantitative SPECT imaging.

Comparison of maximum likelihood and conventional PET scatter scaling methods for 18 F-FDG and 68 Ga-DOTATATE PET/CT.

We aim to quantify differences between a new maximum likelihood (ML) background scaling (MLBS) algorithm and two conventional scatter scaling methods for clinical PET/CT. A common source of reduced image quantification with conventional scatter corrections is attributed to erroneous scaling of the initial scatter estimate to match acquired scattered events in the sinogram. MLBS may have performance advantages over conventional methods by using all available data intersecting the subject. A retrospective analysis was performed on subjects injected with 18 F-FDG (N=71) and 68 Ga-DOTATATE (N=11) and imaged using time-of-flight (TOF) PET/CT. The scatter distribution was estimated with single scatter simulation approaches. Conventional scaling algorithms included (a) tail fitted background scaling (TFBS), which scales the scatter to "tails" outside the emission support, and (b) absolute scatter correction (ABS), which utilizes the simulated scatter distribution with no scaling applied. MLBS consisted of an alternating iterative reconstruction with a TOF-based ML activity image update allowing negative values (NEG-ML) and nested loop ML scatter scaling estimation. Scatter corrections were compared using reconstructed images as follows: (a) normalized relative difference images were generated and used for voxel-wise analysis, (b) liver and suspected lesion ROIs were drawn to compute mean SUVs, and (c) a qualitative analysis of overall diagnostic image quality, impact of artifacts, and lesion conspicuity was performed. Absolute quantification and normalized relative differences were also assessed with an 18 F-FDG phantom study. For human subjects 18 F-FDG data, Bland-Altman plots demonstrated that the largest normalized voxel-wise differences were observed close to the lower limit (SUV=1.0). MLBS reconstructions trended towards higher scatter fractions compared to TFBS and ABS images, with median voxel differences across all subjects for TFBS-MLBS measured at 1.7% and 7.6% for 18 F-FDG and 68 Ga-DOTATATE, respectively. For mean SUV analysis, there was a high degree of correlation between the scatter corrections. For 18 F-FDG, ABS scatter correction reconstructions trended towards higher liver mean SUVs relative to MLBS. The qualitative image analysis revealed no significant differences between TFBS and MLBS image reconstructions. For a uniformly filled relatively large 37cm diameter phantom, MLBS produced the lowest bias in absolute quantification, while normalized voxel-wise differences showed a trend in scatter correction performance consistent with the human subjects study. For 18 F-FDG, MLBS is at least a valid substitute to TFBS, providing reconstructed image performance comparable to TFBS in most subjects but exhibiting quantitative differences in cases where TFBS is typically prone to inaccuracies (e.g., due to patient motion and CT-based attenuation map truncation). Particularly for low contrast regions, quantification differs for ABS compared to MLBS and TFBS, and caution should be taken when utilizing ABS for decision-making based on quantitative metrics.

Approaches to analysing scatter in forming simulations: from fundamental to pragmatic

Including scatter in material properties has received attention in the last decades but, it is not fully mature yet. Industry has cooperated with academia to progress the topic, but at the same time devised simpler ways to start analysis anyway. Robustness analysis is a pre-requisite for process optimisation. Tata Steel has been in material modelling for Sheet Metal Forming for many years and has developed its own yield locus model to enable better customer support. The accuracy of this Vegter model comes at a price, however: more parameters to be measured. Wiebenga devised a robustness analysis but it requires more input than is usually available. At the same time leading software vendors introduced options to evaluate statistical behaviour. Obviously, process optimisation is only useful when accurate models can be employed, so in this paper we will focus on how the scatter in material properties translates in scatter in yield locus for the BBC2005 model vs. Vegter 2017. Automated statistical analysis was not available for Vegter 2017. So, finally, to enable estimation of scatter in forming processes in the short term with Vegter individual simulations were done on a selected number of input datasets. This is shown to give markedly different results to BBC2005.

Evaluation of scatter suppression algorithm for X-ray exposure of soft tissue equivalent phantoms over nominal energy range using FLUKA code

Soft tissue imaging is heavily impaired by streaks and cupping effects associated with X-ray scatter. Quality of images from projection imaging may be improved by the use of enhanced anti-scatter grids’ designs with potency to reject significant scatter. However, optimization of grid characteristics requires investigation to improve diagnostic image quality. Transmitted scatter spatially distributed degrades images engendering need for effective scatter correction protocols. This study investigated the pre-scan scatter suppression algorithm for X-ray exposure of soft tissue equivalent phantoms over nominal energy range. Adipose tissue and polymethyl methacrylate phantoms of cross-sectional area (30 x 30) cm2 and of varying thickness from 2 to 8 cm in 1 cm increments were successively exposed using energy ranging between 20–50 kVp. Monte Carlo simulation based on FLUKA code and flair interface was used to generate an input file for execution. The source simulated five cycles of ten million photons each of annular X-ray photon beam of radius, r = 0.5 cm at fixed field of view (FOV) through anti-scatter grid on to gadolinium oxysulfide detector. The transmitted total, scatter and primary estimates were evaluated with and without grids over varying phantom thicknesses, energy and grid design features. The simulated and experimental results obtained were comparable and in agreement with previous literature. Pearson’s correlation coefficients for scatter fraction and scatter to primary ratio were 0.983 and 0.981, respectively. The strong correlation between simulation and experiment results indicated correctness in methodology and protocol. The algorithms and protocols in the simulation would be appropriate for designing grids with enhanced scatter rejection capabilities.&#x0D; Keywords: FLUKA code, Monte Carlo simulation, Scatter suppression algorithm, Scatter correction, X-ray imaging systems.&#x0D;

The Intrinsic Scatter of Galaxy Scaling Relations

Abstract We present a compendium of disk galaxy scaling relations and a detailed characterization of their intrinsic scatter. Observed scaling relations are typically characterized by their slope, intercept, and scatter; however, these parameters are a mixture of observational errors and astrophysical processes. We introduce a novel Bayesian framework for computing the intrinsic scatter of scaling relations that accounts for nonlinear error propagation and covariant uncertainties. Bayesian intrinsic scatters are ∼25% more accurate than those obtained with a first-order classical method, which systematically underestimates the true intrinsic scatter. Structural galaxy scaling relations based on velocity (V 23.5), size (R 23.5), luminosity (L 23.5), color (g − z), central stellar surface density (Σ1), stellar mass (M *), dynamical mass (M dyn), stellar angular momentum (j *), and dynamical angular momentum (j dyn) are examined to demonstrate the power and importance of the Bayesian formalism. Our analysis is based on a diverse selection of over 1000 late-type galaxies from the Photometry and Rotation Curve Observations from Extragalactic Surveys compilation with deep optical photometry and extended rotation curves. We determine the tightest relation for each parameter by intrinsic orthogonal scatter, finding M * − V 23.5, R 23.5 − j *, and L 23.5 − j dyn to be especially tight. The scatter of the R 23.5 − L 23.5, V 23.5 − (g − z), and R 23.5 − j dyn relations is mostly intrinsic, making them ideal for galaxy formation and evolutionary studies. Our code to compute the Bayesian intrinsic scatter of any scaling relation is also presented. We quantify the correlated nature of many uncertainties in galaxy scaling relations and scrutinize the uncertain nature of disk inclination corrections and their effect on scatter estimates.

Monte-Carlo-Based Estimation of the X-ray Energy Spectrum for CT Artifact Reduction

Beam hardening and scattering effects can seriously degrade image quality in polychromatic X-ray CT imaging. In recent years, polychromatic image reconstruction techniques and scatter estimation using Monte Carlo simulation have been developed to compensate for beam hardening and scattering CT artifacts, respectively. Both techniques require knowledge of the X-ray tube energy spectrum. In this work, Monte Carlo simulations were used to calculate the X-ray energy spectrum of FleXCT, a novel prototype industrial micro-CT scanner, enabling beam hardening and scatter reduction for CT experiments. Both source and detector were completely modeled by Monte Carlo simulation. In order to validate the energy spectra obtained via Monte Carlo simulation, they were compared with energy spectra obtained via a second method. Here, energy spectra were calculated from empirical measurements using a step wedge sample, in combination with the Maximum Likelihood Expectation Maximization (MLEM) method. Good correlation was achieved between both approaches, confirming the correct modeling of the FleXCT system by Monte Carlo simulation. After validation of the modeled FleXCT system through comparing the X-ray spectra for different tube voltages inside the detector, we calculated the X-ray spectrum of the FleXCT X-ray tube, independent of the flat panel detector response, which is a prerequisite for beam hardening and scattering CT artifacts.

A GPU-accelerated framework for rapid estimation of scanner-specific scatter in CT for virtual imaging trials

Virtual imaging trials (VITs), defined as the process of conducting clinical imaging trials using computer simulations, offer a time- and cost-effective alternative to traditional imaging trials for CT. The clinical potential of VITs hinges on the realism of simulations modeling the image acquisition process, where the accurate scanner-specific simulation of scatter in a time-feasible manner poses a particular challenge. To meet this need, this study proposes, develops, and validates a rapid scatter estimation framework, based on GPU-accelerated Monte Carlo (MC) simulations and denoising methods, for estimating scatter in single source, dual-source, and photon-counting CT. A CT simulator was developed to incorporate parametric models for an anti-scatter grid and a curved energy integrating detector with an energy-dependent response. The scatter estimates from the simulator were validated using physical measurements acquired on a clinical CT system using the standard single-blocker method. The MC simulator was further extended to incorporate a pre-validated model for a PCD and an additional source-detector pair to model cross scatter in dual-source configurations. To estimate scatter with desirable levels of statistical noise using a manageable computational load, two denoising methods using a (1) convolutional neural network and an (2) optimized Gaussian filter were further deployed. The viability of this framework for clinical VITs was assessed by integrating it with a scanner-specific ray-tracer program to simulate images for an image quality (Mercury) and an anthropomorphic phantom (XCAT). The simulated scatter-to-primary ratios agreed with physical measurements within 4.4% ± 10.8% across all projection angles and kVs. The differences of ∼121 HU between images with and without scatter, signifying the importance of scatter for simulating clinical images. The denoising methods preserved the magnitudes and trends observed in the reference scatter distributions, with an averaged rRMSE value of 0.91 and 0.97 for the two methods, respectively. The execution time of ∼30 s for simulating scatter in a single projection with a desirable level of statistical noise indicates a major improvement in performance, making our tool an eligible candidate for conducting extensive VITs spanning multiple patients and scan protocols.

Densely sampled spectral modulation for x-ray CT using a stationary modulator with flying focal spot: a conceptual and feasibility study of scatter and spectral correction.

Modulation of the x-ray source in computed tomography (CT) by a designated filter to achieve a desired distribution of photon flux has been greatly advanced in recent years. In this work, we present a densely sampled spectral modulation (DSSM) as a promising low-cost solution to quantitative CT imaging in the presence of scatter. By leveraging a special stationary filter (namely a spectral modulator) and a flying focal spot, DSSM features a strong correlation in the scatter distributions across focal spot positions and sees no substantial projection sparsity or misalignment in data sampling, making it possible to simultaneously correct for scatter and spectral effects in a unified framework. The concept of DSSM is first introduced, followed by an analysis of the design and benefits of using the stationary spectral modulator with a flying focal spot (SMFFS) that dramatically changes the data sampling and its associated data processing. With an assumption that the scatter distributions across focal spot positions have strong correlation, a scatter estimation and spectral correction algorithm from DSSM is then developed, where a dual-energy modulator along with two flying focal spot positions is of interest. Finally, a phantom study on a tabletop cone-beam CT system is conducted to understand the feasibility of DSSM by SMFFS, using a copper modulator and by moving the x-ray tube position in the X direction to mimic the flying focal spot. Based on our analytical analysis of the DSSM by SMFFS, the misalignment of low- and high-energy projection rays can be reduced by a factor of more than 10 when compared with a stationary modulator only. With respect to modulator design, metal materials such as copper, molybdenum, silver, and tin could be good candidates in terms of energy separation at a given attenuation of photon flux. Physical experiments using a Catphan phantom as well as an anthropomorphic chest phantom demonstrate the effectiveness of DSSM by SMFFS with much better CT number accuracy and less image artifacts. The root mean squared error was reduced from 297.9 to 6.5 Hounsfield units (HU) for the Catphan phantom and from 409.3 to 39.2HU for the chest phantom. The concept of DSSM using a SMFFS is proposed. Phantom results on its scatter estimation and spectral correction performance validate our main ideas and key assumptions, demonstrating its potential and feasibility for quantitative CT imaging.

Monte Carlo simulation fused with target distribution modeling via deep reinforcement learning for automatic high-efficiency photon distribution estimation

Particle distribution estimation is an important issue in medical diagnosis. In particular, photon scattering in some medical devices extremely degrades image quality and causes measurement inaccuracy. The Monte Carlo (MC) algorithm is regarded as the most accurate particle estimation approach but is still time-consuming, even with graphic processing unit (GPU) acceleration. The goal of this work is to develop an automatic scatter estimation framework for high-efficiency photon distribution estimation. Specifically, a GPU-based MC simulation initially yields a raw scatter signal with a low photon number to hasten scatter generation. In the proposed method, assume that the scatter signal follows Poisson distribution, where an optimization objective function fused with sparse feature penalty is modeled. Then, an over-relaxation algorithm is deduced mathematically to solve this objective function. For optimizing the parameters in the over-relaxation algorithm, the deep Q -network in the deep reinforcement learning scheme is built to intelligently interact with the over-relaxation algorithm to accurately and rapidly estimate a scatter signal with the large range of photon numbers. Experimental results demonstrated that our proposed framework can achieve superior performance with structural similarity &gt; 0.94 , peak signal-to-noise ratio &gt; 26.55 dB , and relative absolute error &lt; 5.62 % , and the lowest computation time for one scatter image generation can be within 2 s.