Scatter Estimation Research Articles

A unified scatter rejection and correction method for cone beam computed tomography.

Scattered radiation is a major cause of image quality degradation in flat panel detector-based cone beam CT (CBCT). While recently introduced 2D antiscatter grids reject the majority of scatter fluence, the small percentage of scatter fluence still transmitted to the detector remains a major challenge for implementation of quantitative imaging techniques such as dual energy imaging in CBCT. Additionally, this residual scatter is also a major source of grid-induced artifacts, which impedes implementation of 2D grids in CBCT. We therefore present a new method to achieve both robust scatter rejection and residual scatter correction using a 2D antiscatter grid; in doing so, we expand the role of 2D grids from mere scatter rejection devices to scatter measurement devices. In our method, the radiopaque septa of the 2D grid emulate a micro array of beam-stops placed on the detector which introduce spatially periodic septal shadows. By selecting sufficiently thin grid septa, the primary intensity can be reduced while preserving the uniformity of scatter intensity. This enables us to correlate the modulated pixel signal intensity in septal shadows with local scatter intensity. Our method then exploits this correlation to measure and remove residual scatter intensity from projections. No assumptions are made about the object being imaged. We refer to this as Grid-based Scatter Sampling (GSS). In this work, we evaluate the principle of signal modulation with grid septa, the accuracy of scatter estimates, and the effect of the GSS method on image quality using simulations and measurements. We also implement the GSS method experimentally using a 2D grid prototype. Our results demonstrate that the GSS method increased CT number accuracy and reduced image artifacts associated with scatter. With 2D grid and residual scatter correction, HU nonuniformity was reduced from 65HU to 30HU in pelvis sized phantoms, and HU variations due to change in phantom size were reduced from 59HU to 20HU, when compared to use of only a 2D grid. With residual scatter correction via GSS method, grid-induced ring artifacts were suppressed, leading to a 41% reduction in noise. The shape of the modulation transfer function (MTF) was preserved before and after suppression of ring artifacts. Our grid-based scatter sampling method enables utilization of a 2D grid as a scatter measurement and correction device. This method significantly improves quantitative accuracy in CBCT, further reducing the image quality gap between CBCT and multi-detector CT. By correcting residual scatter with the proposed method, grid-induced line artifacts in projections and associated ring artifacts in CBCT images were also suppressed with no compromise of spatial resolution.

Radar imaging with EISCAT 3D

Abstract. A new incoherent scatter radar called EISCAT 3D is being constructed in northern Scandinavia. It will have the capability to produce volumetric images of ionospheric plasma parameters using aperture synthesis radar imaging. This study uses the current design of EISCAT 3D to explore the theoretical radar imaging performance when imaging electron density in the E region and compares numerical techniques that could be used in practice. Of all imaging algorithms surveyed, the singular value decomposition with regularization gave the best results and was also found to be the most computationally efficient. The estimated imaging performance indicates that the radar will be capable of detecting features down to approximately 90×90 m at a height of 100 km, which corresponds to a ≈0.05∘ angular resolution. The temporal resolution is dependent on the signal-to-noise ratio and range resolution. The signal-to-noise ratio calculations indicate that high-resolution imaging of auroral precipitation is feasible. For example, with a range resolution of 1500 m, a time resolution of 10 s, and an electron density of 2×1011m-3, the correlation function estimates for radar scatter from the E region can be measured with an uncertainty of 5 %. At a time resolution of 10 s and an image resolution of 90×90 m, the relative estimation error standard deviation of the image intensity is 10 %. Dividing the transmitting array into multiple independent transmitters to obtain a multiple-input–multiple-output (MIMO) interferometer system is also studied, and this technique is found to increase imaging performance through improved visibility coverage. Although this reduces the signal-to-noise ratio, MIMO has successfully been applied to image strong radar echoes as meteors and polar mesospheric summer echoes. Use of the MIMO technique for incoherent scatter radars (ISRs) should be investigated further.

Matched and Mismatched Estimation of Kronecker Product of Linearly Structured Scatter Matrices Under Elliptical Distributions

The estimation of covariance matrices is a core problem in many modern adaptive signal processing applications. For matrix- and array-valued data, e.g., MIMO communication, EEG/MEG (time versus channel), the covariance matrix of vectorized data may belong to the non-convex set of Kronecker product structure. In addition, the Kronecker factors can also exhibit an additional linear structure. Taking this prior knowledge into account during the estimation process drastically reduces the amount of unknown parameters, and then improves the estimation accuracy. On the other hand, the broad class of complex elliptically symmetric distributions, as well as the related complex angular elliptical distribution, are particularly suited to model heavy-tailed multivariate data. In this context, we first establish novel robust estimators of scatter and shape matrices (both related to a covariance matrix), having a Kronecker product structure with linearly structured Kronecker factors. Then, we conduct a theoretical analysis of their asymptotic performance (i.e., consistency, asymptotic distribution and efficiency), in matched and mismatched scenarios, i.e., when misspecifications between the true and assumed models occur. Finally, numerical results illustrate the theoretical analysis and assess the usefulness of the proposed estimators.

Optimization of scatter estimation window setting for quantitative analysis in 111 In-pentetreotide single photon emission computed tomography imaging.

The aim of this study was to validate the optimal scatter correction method and scatter estimation window setting in terms of image quality and quantitative accuracy for quantitative indium-111 (111In)-pentetreotide SPECT imaging. We used a positron emission tomography/computed tomography (PET/CT) phantom to validate image quality and quantitative accuracy, and the SPECT images were acquired by the multi-energy window (MEW) method. The scatter estimation was performed using four kinds of energy windows (MEW1, MEW2, MEW3, and MEW4). Scatter correction was also performed using a dual-energy window (DEW) for comparison with MEWs. Image quality was assessed using percent contrast (% contrast) and background variability, and quantitative accuracy was assessed using the mean standardized uptake value (SUVmean) with hot spheres. In the quantification, all MEW settings approached the theoretical SUVmean (MEW1, 0.99±0.06; MEW2, 0.99±0.05; MEW3, 1.00±0.08; MEW4, 0.97±0.12) in contrast to DEW (0.88±0.05). The SUVmean value for scatter correction of both photopeaks for a 28 mm sphere showed the smallest difference from the theoretical value. The scatter correction method that gave optimal image quality and quantitative accuracy was MEW3 with two 20% energy windows (one over each photopeak) and four adjacent 3% scatter estimation windows (one on each side of the two photopeaks).

Practical joint reconstruction of activity and attenuation with autonomous scaling for time-of-flight PET

Recent research has showed that attenuation images can be determined from emission data, jointly with activity images, up to a scaling constant when utilizing the time-of-flight (TOF) information. We aim to develop practical CT-less joint reconstruction for clinical TOF PET scanners to obtain quantitatively accurate activity and attenuation images. In this work, we present a joint reconstruction of activity and attenuation based on MLAA (maximum likelihood reconstruction of attenuation and activity) with autonomous scaling determination and joint TOF scatter estimation from TOF PET data. Our idea for scaling is to use a selected volume of interest (VOI) in a reconstructed attenuation image with known attenuation, e.g. a liver in patient imaging. First, we construct a unit attenuation medium which has a similar, though not necessarily the same, support to the imaged emission object. All detectable LORs intersecting the unit medium have an attenuation factor of e −1≈ 0.3679, i.e. the line integral of linear attenuation coefficients is one. The scaling factor can then be determined from the difference between the reconstructed attenuation image and the known attenuation within the selected VOI normalized by the unit attenuation medium. A four-step iterative joint reconstruction algorithm is developed. In each iteration, (1) first the activity is updated using TOF OSEM from TOF list-mode data; (2) then the attenuation image is updated using XMLTR—a extended MLTR from non-TOF LOR sinograms; (3) a scaling factor is determined based on the selected VOI and both activity and attenuation images are updated using the estimated scaling; and (4) scatter is estimated using TOF single scatter simulation with the jointly reconstructed activity and attenuation images. The performance of joint reconstruction is studied using simulated data from a generic whole-body clinical TOF PET scanner and a long axial FOV research PET scanner as well as 3D experimental data from the PennPET Explorer scanner. We show that the proposed joint reconstruction with proper autonomous scaling provides low bias results comparable to the reference reconstruction with known attenuation.

Deep Network for Scatterer Distribution Estimation for Ultrasound Image Simulation.

Simulation-based ultrasound (US) training can be an essential educational tool. Realistic US image appearance with typical speckle texture can be modeled as convolution of a point spread function with point scatterers representing tissue microstructure. Such scatterer distribution, however, is in general not known and its estimation for a given tissue type is fundamentally an ill-posed inverse problem. In this article, we demonstrate a convolutional neural network approach for probabilistic scatterer estimation from observed US data. We herein propose to impose a known statistical distribution on scatterers and learn the mapping between US image and distribution parameter map by training a convolutional neural network on synthetic images. In comparison with several existing approaches, we demonstrate in numerical simulations and with in vivo images that the synthesized images from scatterer representations estimated with our approach closely match the observations with varying acquisition parameters such as compression and rotation of the imaged domain.

Real-time discriminant analysis in the presence of label and measurement noise

Quadratic discriminant analysis (QDA) is a widely used classification technique. Based on a training dataset, each class in the data is characterized by an estimate of its center and shape, which can then be used to assign unseen observations to one of the classes. The traditional QDA rule relies on the empirical mean and covariance matrix. Unfortunately, these estimators are sensitive to label and measurement noise which often impairs the model’s predictive ability. Robust estimators of location and scatter are resistant to this type of contamination. However, they have a prohibitive computational cost for large scale industrial experiments. We present a novel QDA method based on a recent real-time robust algorithm. We additionally integrate an anomaly detection step to classify the most atypical observations into a separate class of outliers. Finally, we introduce the label bias plot, a graphical display to identify label and measurement noise in the training data. The performance of the proposed approach is illustrated in a simulation study with huge datasets, and on real datasets about diabetes and fruit.

Markov matrixes for random sequences imitation in fatigue testing and design in the problem of safety of steel structures

To guarantee the safety of steel structures it is important to deal properly with the problem of representation of exploitation loading. For metal fatigue testing and design, the proper choice of random (irregular) loading type is very important. The principles of random loading are discussed and some alternative approaches with their pros and cons are shortly reviewed in the paper. As a sound decision for random, but taking into account some specific features of the exploitation loading process, the target Markov method is proposed. According to this method, the important information of the real random processes in the form of the turning point is used for filling the square Markov matrix (analysis phase) and later on, with employing the random number generator, serves as a source for creating of the so-called replicas. The replicas are the random trial for numerical estimation of longevity scatter. Due to the fact, that all these manipulations are performed with the aim of metal fatigue investigation, some important processes’ characteristics for fatigue, like irregularity factor, fullness factor and machine part longevities were compared. Some important suggestion for the future development of this method, that is taking into consideration the sequence of the events, is discussed.

Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

Both cell-wise and case-wise outliers may appear in a real data set at the same time. Few methods have been developed in order to deal with both types of outliers when formulating a regression model. In this work, a robust estimator is proposed based on a three-step method named 3S-regression, which uses the comedian as a highly robust scatter estimate. An intensive simulation study is conducted in order to evaluate the performance of the proposed comedian 3S-regression estimator in the presence of cell-wise and case-wise outliers. In addition, a comparison of this estimator with recently developed robust methods is carried out. The proposed method is also extended to the model with continuous and dummy covariates. Finally, a real data set is analyzed for illustration in order to show potential applications.

Iterative Algorithms for Joint Scatter and Attenuation Estimation From Broken Ray Transform Data

The single-scatter approximation is fundamental in many tomographic imaging problems including x-ray scatter imaging and optical scatter imaging for certain media. In all cases, noisy measurements are affected by both local scatter events and nonlocal attenuation. Prior works focus on reconstructing one of two images: scatter density or total attenuation. However, both images are media specific and useful for object identification. Nonlocal effects of the attenuation image on the data are summarized by the broken ray transform (BRT). While analytic inversion formulas exist, poor conditioning of the inverse problem is only exacerbated by noisy measurements and sampling errors. This has motivated interest in the related star transforms incorporating BRT measurements from multiple source-detector pairs. However, all analytic methods operate on the log of the data. For media comprising regions with no scatter a new approach is required. We are the first to present a joint estimation algorithm based on Poisson data models for a single-scatter measurement geometry. Monotonic reduction of the log-likelihood function is guaranteed for our iterative algorithm while alternating image updates. We also present a fast algorithm for computing the discrete BRT forward operator. Our generalized approach can incorporate both transmission and scatter measurements from multiple source-detector pairs. Transmission measurements resolve low-frequency ambiguity in the joint image estimation problem, while multiple scatter measurements resolve the attenuation image. The benefits of joint estimation, over single-image estimation, vary with problem scaling. Our results quantify these benefits and should inform design of future acquisition systems.

Regularized minimal residual method for permittivity reconstruction in microwave imaging

AbstractIn this paper, a regularized reconstruction based on the minimal residual method is proposed for microwave imaging applications. The method provides optimum regularization parameter to estimate the distribution of permittivity values of unknown scatterers under test. Initially, the method is applied to Born approximated linear model for weak scatterers. The performance of this approach is compared with the commonly adopted Morozov's discrepancy principle used in conjunction with the Tikhonov regularization. The effectiveness of the method is assisted by simulating the various numerical examples of synthetic and experimental data. The results of numerical simulations validate that the proposed method is highly effective. Thereafter, a non‐linear inverse problem based on the inexact Newton method is examined for the estimation of strong scatterers. Here also, the proposed method is found to be helpful in terms of improving the image accuracy.

Probabilistic Low Cycle Fatigue criterion for nodular cast-irons

This paper proposes an original method for characterising the Low Cycle Fatigue (LCF) lifetime using probability density functions. The protocol is based on statistics of microstructure heterogeneities taken as damage initiation sites, a qualitative mechanical analysis of the heterogeneities harmfulness and the definition of a micro-crack growth law. The technique is here established and the associated model identified for a nodular cast iron where the graphite nodules are assumed to be the damage initiation zones. The LCF lifetime is characterised from both a large set of experimental test between 300 and 600 °C and damage observations at the micro-scale. Experimental post-mortem observation combined with an expanded literature review first enable to assume the harmfulness of nodules according to their size and their probable role in the damage process A probability density function for the lifetime is then built from the following steps: (i) a quantitative analysis of the material micro-structure, which provides the probability density of nodules occurrence depending of their size (ii) an extreme value analysis using a Gumbel distribution and (iii) a micro-crack growth law associated with LCF conventional terms of energy densities. Its parameters are obtained using an optimisation process applied to laboratory fatigue experiment. The obtained probability function provides a good match for the lifetime and greatly improves results given by conventional criteria. It moreover provides a robust estimate of the lifetime scatter for different types of fatigue tests.

English

Scatter halfspace depth is a statistical tool that allows one to quantify the fitness of a candidate covariance matrix with respect to the scatter structure of a probability distribution. The depth enables simultaneous robust estimation of location and scatter, and nonparametric inference on these. A handful of remarks on the definition and the properties of the scatter halfspace depth are provided. It is argued that the currently used notion of this depth is well suited especially for symmetric random vectors. The scatter halfspace depth closely relates to an appropriate distance of matrix-generated ellipsoids from an upper level set of the (location) halfspace depth function. Several modifications and extensions to the scatter halfspace depth are considered, with their theoretical properties outlined.

A deep neural network for fast and accurate scatter estimation in quantitative SPECT/CT under challenging scatter conditions.

A major challenge for accurate quantitative SPECT imaging of some radionuclides is the inadequacy of simple energy window-based scatter estimation methods, widely available on clinic systems. A deep learning approach for SPECT/CT scatter estimation is investigated as an alternative to computationally expensive Monte Carlo (MC) methods for challenging SPECT radionuclides, such as 90Y. A deep convolutional neural network (DCNN) was trained to separately estimate each scatter projection from the measured 90Y bremsstrahlung SPECT emission projection and CT attenuation projection that form the network inputs. The 13-layer deep architecture consisted of separate paths for the emission and attenuation projection that are concatenated before the final convolution steps. The training label consisted of MC-generated "true" scatter projections in phantoms (MC is needed only for training) with the mean square difference relative to the model output serving as the loss function. The test data set included a simulated sphere phantom with a lung insert, measurements of a liver phantom, and patients after 90Y radioembolization. OS-EM SPECT reconstruction without scatter correction (NO-SC), with the true scatter (TRUE-SC) (available for simulated data only), with the DCNN estimated scatter (DCNN-SC), and with a previously developed MC scatter model (MC-SC) were compared, including with 90Y PET when available. The contrast recovery (CR) vs. noise and lung insert residual error vs. noise curves for images reconstructed with DCNN-SC and MC-SC estimates were similar. At the same noise level of 10% (across multiple realizations), the average sphere CR was 24%, 52%, 55%, and 67% for NO-SC, MC-SC, DCNN-SC, and TRUE-SC, respectively. For the liver phantom, the average CR for liver inserts were 32%, 73%, and 65% for NO-SC, MC-SC, and DCNN-SC, respectively while the corresponding values for average contrast-to-noise ratio (visibility index) in low-concentration extra-hepatic inserts were 2, 19, and 61, respectively. In patients, there was high concordance between lesion-to-liver uptake ratios for SPECT reconstruction with DCNN-SC (median 4.8, range 0.02-13.8) compared with MC-SC (median 4.0, range 0.13-12.1; CCC = 0.98) and with 90Y PET (median 4.9, range 0.02-11.2; CCC = 0.96) while the concordance with NO-SC was poor (median 2.8, range 0.3-7.2; CCC = 0.59). The trained DCNN took ~ 40s (using a single i5 processor on a desktop computer) to generate the scatter estimates for all 128 views in a patient scan, compared to ~ 80min for the MC scatter model using 12 processors. For diverse 90Y test data that included patient studies, we demonstrated comparable performance between images reconstructed with deep learning and MC-based scatter estimates using metrics relevant for dosimetry and for safety. This approach that can be generalized to other radionuclides by changing the training data is well suited for real-time clinical use because of the high speed, orders of magnitude faster than MC, while maintaining high accuracy.

Efficient staircase testing of probabilistic Haigh diagrams

In this work, high cycle fatigue test programs based on staircase schemes at multiple mean stress levels are analyzed statistically with respect to their capability of estimating the parameters of a parameterized probabilistic Haigh diagram. Given a fixed number of tests, the influence of the used test specimen geometry, number of mean stress levels, step size and initial stresses are investigated. The central result shows that test programs which contain tests with both smooth and notched specimens lead to a considerable improvement of the fatigue strength scatter estimate compared to test programs using only one test specimen geometry.

Late Miocene to late Pleistocene geomagnetic secular variation at high northern latitudes

SUMMARYWe report a palaeomagnetic study of Icelandic lavas of late Miocene to late Pliocene age to test the geocentric axial dipole hypothesis at high northern latitudes. Cores were sampled from 125 sites in the Fljótsdalur valley in eastern Iceland, and hand samples were taken for 17 new incremental heating 40Ar/39Ar age determinations. 96 per cent of the cores were oriented using both a Brunton compass and a sun compass. Comparison of the magnetic and sun azimuths reveals deviations of ±5°, ±10° and ±20°, respectively, for 42, 16 and 3 per cent of the data points, indicating that core sampling intended for palaeosecular variation (PSV) studies at high northern latitudes should be oriented by sun. A total of 1279 independent specimens were subjected to AF- and thermal-demagnetization for palaeodirectional analysis, and well-grouped site mean directions were obtained for 123 sites of which 113 were found to be independent sites. Applying a selection criteria of k > 50 and N ≥ 5 (Nmean = 9.5), we obtain a combined grand mean direction for 46 normal and 53 reverse (for VGPlat > ±45°) polarity sites of declination = 5.6° and inclination = 77.5° that is not significantly different from that expected from a GAD field. The corresponding palaeomagnetic pole position (VGPlat = 86.3°N, VGPlon = 21.2°E, dp/dm = 4.0°/4.3°) is coincident with the North Pole within the 95 per cent confidence limits. An updated age model is constructed based on the 40Ar/39Ar ages, showing that the majority of the Fljótsdalur lavas fall within 2–7 Ma. We combine the Fljótsdalur data with existing data from the nearby Jökuldalur valley. The 154 palaeodirections are well-dispersed between 1 and 7 Ma and constitute a high-quality data set for PSV analysis. Our results partly support previous conclusions of a generally higher dispersion during reverse polarity intervals. However, when comparing our Matutayma data with Brunhes age data from Jan Mayen, we find no evidence of a higher VGP scatter during the Matuyama as previously suggested. When comparing our VGP scatter to the two commonly used models for VGP dispersion: Model G and TK03, we find a good fit for all 1–7 Ma VGP scatter data SB(1–7) to Model G, whereas SB(1–7) is not fitted by TK03, even when considering the uncertainty of SB(1–7). We also find that all VGP scatter estimates, except that for the Gilbert subset, are consistent with Model G, while the discrepancy with TK03 is generally larger.

Evaluation of the diet based on the variability of the food composition data

Nutrient composition is a necessary part in the assessing of nutritional value of diets and new foods. According to the results of comparison of nutrient value of the diet with daily requirements the judgment on compliance of the diet (or product) to norm or deviation from the standard is taken out. In the interpretation of the term "value corresponds to the norm" in modern practice, only average values are used, while the content of nutrients in food is not described by fixed values, but has a statistical nature, which creates difficulties in the conscientious development of diets and their harmonization in sanitary authorities. Specifying a range of normative values (±5-10%) does not provide a valid solution. The aim of the research was to assess the size of the spread of nutrient content for the diet as a whole and to use this estimate in relation to the task of "comparing the actual value and the norm". Material and methods. In this work, we used the method of mathematical modeling of recipes, the calculation of nutrient content based on that of ingredients, and reference publications on the nutrient composition of products and collections of recipes were used as starting materials. Results and discussion. The calculation of nutrient composition according to the recipe is described, taking into account not only average values, but also scatter indicators (error) of nutrient content values, which makes it possible to reasonably make judgments about the compliance of the actual value with the established reference value. The calculation of estimates of the spread of nutrient composition values using the information about the error of the initial data on the nutrient composition of the products, the output of the absolute and relative error in the formulation and the whole diet was described. Examples of calculations of scatter estimates are given: for one recipe/ nutrient (primary); calculation for days and mealtimes; for a day of a cyclic menu and for a 4-week cycle of school meals menus (primary and secondary school age). The mapping of the variables having a statistical nature has been graphically showed, the measure of estimating the proximity of the values of the statistical nature has been proposed discrete and continuous. Comparison of indicators of variability of domestic and foreign reference databases, mapping information about variation in the types of meals, differences in the extent of variation in the nutrients has been given. Conclusions. The conclusions are formulated on the need for statistical presentation of consumption reference values for research for various reasons of variability, on the need to take statistics into account for the system of accumulating data on nutrient composition in databases.

Enhancement of soft-tissue contrast in cone-beam CT using an anti-scatter grid with a sparse sampling approach

PurposeAnti-scatter grids suppress the scatter substantially thus improving image contrast in radiography. However, its active use in cone-beam CT for the purpose of improving contrast-to-noise ratio (CNR) has not been successful mainly due to the increased noise related to Poisson statistics of photons. This paper proposes a sparse-view scanning approach to address the above issue. MethodCompared to the conventional cone-beam CT imaging framework, the proposed method reduces the number of projections and increases exposure in each projection to enhance image quality without an additional cost of radiation dose to patients. For image reconstruction from sparse-view data, an adaptive-steepest-descent projection-onto-convex-sets (ASD POCS) algorithm regularized by total-variation (TV) minimization was adopted. Contrast and CNR with various scattering conditions were evaluated in projection domain by a simulation study using GATE. Then we evaluated contrast, resolution, and image uniformity in CT image domain with Catphan phantom. A head phantom with soft-tissue structures was also employed for demonstrating a realistic application. A virtual grid-based estimation and reduction of scatter has also been implemented for comparison with the real anti-scatter grid. ResultsIn the projection domain evaluation, contrast and CNR enhancement was observed when using an anti-scatter grid compared to the virtual grid. In the CT image domain, the proposed method produced substantially higher contrast and CNR of the low-contrast structures with much improved image uniformity. ConclusionWe have shown that the proposed method can provide high-quality CBCT images particularly with an increased contrast of soft-tissue at a neutral dose for image-guidance.

High-Quality MicroCT Rock Imaging: Methodology To Measure and Correct for X-Ray Scatter

Summary Microcomputed tomography (microCT) of cores yields valuable information about rock and fluid properties at pore scale for conventional rock and at rock heterogeneity scale for unconventionals. High levels of uncorrected X-ray scatter in computed tomography (CT) data lead to strong image artifacts and erroneous Hounsfield unit (HU) values, making reconstructed images unsuitable for accurate digital rock (DR) characterization (e.g., segmentation, material decomposition, and others). MicroCT scanners do not include scatter correction techniques. To fill this gap, we developed a new methodology to measure and remove the scatter component from raw projection microCT data collected during rock core scans, and ultimately improving the image quality of scanned cores. Widely used approaches for scatter estimation, based on Monte Carlo (MC) simulations and simplified analytical models, are time-consuming and may lose accuracy when imaging complex unconventional shale cores. In this paper, we propose a more practical approach to perform scatter correction from direct scatter measurements, an approach that is based on the beam-stop array (BSA) method. The BSA method works as follows: The radiation scattered by the core sample is emitted in random directions. By placing an array of small, highly absorbing beads between the source and the core, the primary X-ray signal through the beads is blocked, but the overall object scatter signal is not affected. The observed values in the beads’ shadows on the detector are assumed to be scatter signal. Performing interpolation of the scatter signal between the shadowed by beads pixels on the detector gives an estimate of the scatter signal at every pixel on the detector. Subtracting scatter from projection data yields scatter-corrected data used for 3D CT core image reconstruction. To develop the core scatter correction methodology, we executed the following three tasks: (1) performed modeling of primary and scattered signals to optimize the BSA design (beads size and layout) and scan parameters; (2) developed and implemented an accurate scatter correction algorithm into our 3D microCT image reconstruction workflow; and (3) tested the proposed methodology using four shale core samples from the United States and the Middle East. To better assess the impact of scatter, all experiments with shale core plugs presented in this paper were conducted using source energy of 160 kVp. Our results demonstrated that in many cases, especially with higher attenuating cores, failing to correct for X-ray scatter may result in significant loss of image reconstruction accuracy. We also showed that the developed methodology allows for accurate estimation and removal of scatter from the raw (projection) CT data, enabling reconstruction of high-quality core images that are required for performing DR analysis. To assess the impact of X-ray scatter on the accuracy of DR segmentation, we compared the amount of resolved air-filled space using a stack of image slices by thresholding for the air regions. Our results showed that the amount of detected air-filled space may increase significantly when scatter correction is applied. The presented scatter correction methodology is general and can be used with any microCT scanner used by the petroleum industry to improve image quality and derive accurate HU values. This is of significant importance for quantitative characterization of highly heterogeneous rock with fine structural changes, as is the case for shale. Ultimately, this methodology should expand the operational envelope and value of microCT imaging in the exploration and production workflows.

A Novel Method for Abrupt Motions Estimation of Sparse Scatterers in Differential Tomography SAR Imaging

AbstractIn urban areas with many buildings, the scatterers located within one pixel can be assumed to be discrete and sparse (m = 0, 1, or 2). When the abrupt motions of sparse scatterers only happen in a single synthetic aperture radar (SAR) acquisition, these motions cannot be calculated using 2‐D or 3‐D frequency spectrum estimation method based on traditional differential Tomography SAR model. In this paper, a novel approach is proposed to solve this issue. By compensating a phase factor from the acquisition which has an abrupt motion and then maximizing the 3D Elevation‐Linear motion‐Amplitude of periodic motion spectrum at the scatterers locations, the final abrupt motions of the scatterers could be calculated. For the scatterers simulated, the estimation accuracy of the locations along elevation direction, linear motions velocity, the amplitudes of seasonal periodic motions, the amplitudes of relative scattering values, and the abrupt motions in the last acquisition are shown. The simulation results demonstrate that the proposed method can achieve high accuracy for no‐noise situation. The root‐mean‐square errors of the abrupt motions estimation are also acceptable (about 1–2 mm) when the signal‐to‐noise ratio = 10 and 8 dB. Thus, the estimation accuracy of the proposed algorithm can also fulfill the practical applications requirement.