Algebraic Reconstruction Technique Research Articles

Estimation of anisotropy parameters in vertical transverse isotropy media using the ray‐based tomography

AbstractIn seismic exploration, it is very important to consider the presence of anisotropy in order to image the subsurface correctly. The knowledge of anisotropic parameters leads to more precise characterization of reservoir, fracture density and flow paths. However, conventional geophysical methods do not directly measure these parameters, and it is useful to have a method to estimate them from seismic data. In the weak transverse isotropy approximation, the fields to be considered are the vertical and horizontal velocity components and the Thomsen parameters and . We present a method for estimating the anisotropic Thomsen parameters in the presence of weak vertical transverse isotropy using P‐wave traveltime tomography based on anisotropic ray tracing. Depending on the available information, we propose different approaches to retrieve the unknowns. A conventional three‐dimensional traveltime tomography algorithm has been extended to include anisotropic ray tracing and using the algebraic reconstruction technique or modified simultaneous iterative reconstruction technique to retrieve the unknowns. We test the method on synthetic examples for the inversion of transmitted and reflected traveltimes, and we evaluate the sensitivity of the tomographic results to the available information. Furthermore, we also consider the case of tilted transverse isotropy in a seismic reflection example.

Sparse-View Neutron Computed Tomography 3-D Reconstruction via the Fast Gradient Projection Algorithm

Neutron tomography is an efficient nondestructive testing technique. As a complement to X-ray computed tomography, it has been widely used in various fields. Due to the difficulty of obtaining complete neutron projection data in a high-radiation environment and the high noise characteristics of neutron images, it is difficult to reconstruct a high-quality image using the conventional filtered-back projection (FBP) algorithm. Therefore, research on sparse-view reconstruction algorithms in neutron tomography is needed. To improve the quality of neutron three-dimensional reconstructed images, this paper proposes an algorithm that combines the Simultaneous Algebraic Reconstruction Technique (SART) with Fast Gradient Projection (FGP), where the FGP is an algorithm for image denoising and deblurring based on the discrete total variation (TV) minimization model. The algorithm proposed in this paper is compared with other algorithms (FBP, SART, and SART-TV) by simulated experimental data and real neutron experimental data. The experimental results show that the novel algorithm outperforms the other three algorithms in terms of denoising and retaining detailed structural information.

Motion compensated cone-beam CT reconstruction using an a priori motion model from CT simulation: a pilot study

Objective. To combat the motion artifacts present in traditional 4D-CBCT reconstruction, an iterative technique known as the motion-compensated simultaneous algebraic reconstruction technique (MC-SART) was previously developed. MC-SART employs a 4D-CBCT reconstruction to obtain an initial model, which suffers from a lack of sufficient projections in each bin. The purpose of this study is to demonstrate the feasibility of introducing a motion model acquired during CT simulation to MC-SART, coined model-based CBCT (MB-CBCT). Approach. For each of 5 patients, we acquired 5DCTs during simulation and pre-treatment CBCTs with a simultaneous breathing surrogate. We cross-calibrated the 5DCT and CBCT breathing waveforms by matching the diaphragms and employed the 5DCT motion model parameters for MC-SART. We introduced the Amplitude Reassignment Motion Modeling technique, which measures the ability of the model to control diaphragm sharpness by reassigning projection amplitudes with varying resolution. We evaluated the sharpness of tumors and compared them between MB-CBCT and 4D-CBCT. We quantified sharpness by fitting an error function across anatomical boundaries. Furthermore, we compared our MB-CBCT approach to the traditional MC-SART approach. We evaluated MB-CBCT’s robustness over time by reconstructing multiple fractions for each patient and measuring consistency in tumor centroid locations between 4D-CBCT and MB-CBCT. Main results. We found that the diaphragm sharpness rose consistently with increasing amplitude resolution for 4/5 patients. We observed consistently high image quality across multiple fractions, and observed stable tumor centroids with an average 0.74 ± 0.31 mm difference between the 4D-CBCT and MB-CBCT. Overall, vast improvements over 3D-CBCT and 4D-CBCT were demonstrated by our MB-CBCT technique in terms of both diaphragm sharpness and overall image quality. Significance. This work is an important extension of the MC-SART technique. We demonstrated the ability of a priori 5DCT models to provide motion compensation for CBCT reconstruction. We showed improvements in image quality over both 4D-CBCT and the traditional MC-SART approach.

Improving depth uncertainty in plenoptic camera-based velocimetry

This work describes the development of a particle tracking velocimetry (PTV) algorithm designed to improve three-dimensional (3D), three-component velocity field measurements using a single plenoptic camera. Particular focus is on mitigating the longstanding depth uncertainty issues that have traditionally plagued plenoptic particle image velocimetry (PIV) experiments by leveraging the camera’s ability to generate multiple perspective views of a scene in order to assist both particle triangulation and tracking. 3D positions are first estimated via light field ray bundling (LFRB) whereby particle rays are projected into the measurement volume using image-to-object space mapping. Tracking is subsequently performed independently within each perspective view, providing a statistical amalgamation of each particle’s predicted motion through time in order to help guide 3D trajectory estimation while simultaneously protecting the tracking algorithm from physically unreasonable fluctuations in particle depth positions. A synthetic performance assessment revealed a reduction in the average depth errors obtained by LFRB as compared to the conventional multiplicative algebraic reconstruction technique when estimating particle locations. Further analysis using a synthetic vortex ring at a magnification of − 0.6 demonstrated plenoptic-PIV capable of maintaining the equivalent of 0.1–0.15 voxel accuracy in the depth domain at a spacing to displacement ratio of 5.3–10.5, an improvement of 84–89% compared to plenoptic-PIV. Experiments were conducted at a spacing to displacement ratio of approximately 5.8 to capture the 3D flow field around a rotor within the rotating reference frame. The resulting plenoptic-PIV/PTV vector fields were evaluated with reference to a fixed frame stereoscopic-PIV (stereo-PIV) validation experiment. A systematic depth-wise (radial) component of velocity directed toward the wingtip, consistent with observations from prior literature and stereo-PIV experiments, was captured by plenoptic-PTV at magnitudes similar to the validation data. In contrast, the plenoptic-PIV did not discern any coherent indication of radial motion. Our algorithm constitutes a significant advancement in enhancing the functionality and versatility of single-plenoptic camera flow diagnostics by directly addressing the primary limitation associated with plenoptic imaging.Graphical abstract

Vertical Distribution Mapping for Methane Fugitive Emissions Using Laser Path-Integral Sensing in Non-Cooperative Open Paths.

Observing the vertical diffusion distribution of methane fugitive emissions from oil/gas facilities is significant for predicting the pollutant's spatiotemporal transport and quantifying the random emission sources. A method is proposed for methane's vertical distribution mapping by combining the laser path-integral sensing in non-non-cooperative open paths and the computer-assisted tomography (CAT) techniques. It uses a vertical-plume-mapping optical path configuration and adapts the developed dynamic relaxation and simultaneous algebraic reconstruction technique (DR-SART) into methane-emission-distribution reconstruction. A self-made miniaturized TDLAS telemetry sensor provides a reliable path to integral concentration information in non-non-cooperative open paths, with Allan variance analysis yielding a 3.59 ppm·m sensitivity. We employed a six-indexes system for the reconstruction performance analysis of four potential optical path-projection configurations and conducted the corresponding validation experiment. The results have shown that that of multiple fan-beams combined with parallel-beam modes (MFPM) is better than the other optical path-projection configurations, and its reconstruction similarity coefficient (ε) is at least 22.4% higher. For the different methane gas bag-layout schemes, the reconstruction errors of maximum concentration (γm) are consistently around 0.05, with the positional errors of maximum concentration (δ) falling within the range of 0.01 to 0.025. Moreover, considering the trade-off between scanning duration and reconstruction accuracy, it is recommended to appropriately extend the sensor measurement time on a single optical path to mitigate the impact of mechanical vibrations induced by scanning motion.

MUYSC: an end-to-end muography simulation toolbox

SUMMARY Muography is an imaging technique that relies on the attenuation of the muon flux traversing geological or anthropogenic structures. Several simulation frameworks help to perform muography studies by combining specialized codes: for muon generation through muon transport to muon detector performance. This methodology is precise but requires significant computational resources and time. We present an end-to-end python-based MUographY Simulation Code, which implements a muography simulation framework capable of rapidly estimating muograms of any geological structure worldwide. This framework considers the generated muon flux as the observation point; the energy loss of muons passing through the geological target; the integrated muon flux detected by the telescope and estimates the 3-D density distribution of the target using algebraic reconstruction techniques. The simulations ignore the relatively small muon flux variance caused by geomagnetic effects, solar modulation and atmospheric conditions. We validate the code performance by comparing our simulation results with data from other frameworks.

Estimation of pollutant source using source-receptor response matrix from maximum-length sequence pulse technique

Accurate estimation of pollutant sources in built environments is crucial for monitoring air quality and preventing harm to health and property. This study presented an improved method for estimating the dynamical pollutant source strength using the concentration signal monitored at the receptor point. We employed a built environment system subjected to a pollutant pulse signal in accordance with the maximum-length sequence (m-sequence) to acquire response concentration. Subsequently, the source-receptor response matrix was inversely identified based on the known pulse signal and the response concentration. Then, the unknown source release rate was inversely estimated by the monitored concentration signal and previously identified response matrix. In addition, the performances of different inverse algorithms and m-sequence orders were also analyzed. Here both simulation and application to a real experiment of a wind duct were implemented, and the results demonstrated the higher-order m-sequence method exhibited better noise resistance compared to the traditional unit pulse method. In both simulation and experiment, the m-sequence pulse method reduced the root mean square error (RMSE) by 39.9 % and 70.7 %, respectively, compared to the unit pulse method. In experiment, the simultaneous multiplicative algebraic reconstruction technique (SMART) combined with the Tikhonov regularization (TR) method showed relatively stable performance.

Improvement of the longitudinal phase space tomography at the J-PARC synchrotrons

The longitudinal phase space tomography, which reconstructs the phase space distribution from the one-dimensional bunch profiles, is used in various accelerators to measure longitudinal beam parameters. At the J-PARC, an implementation of the phase space tomography based on the Convolution Back Projection method (CBP) has been used to measure the momentum spread of the injected beam. The method assumes that the beam distribution rotates without significant deformation during the synchrotron oscillation. Because of the nonlinearity of synchrotron motion with sinusoidal RF voltage, the method can be used only in limited situations such as small amplitude synchrotron oscillation. Algebraic Reconstruction Techniques (ART) in conjunction with particle tracking, which is implemented in the CERN’s tomography code, allows accurate reconstructions even for nonlinear large amplitude synchrotron oscillations. We present the overview of the application of the CERN’s tomography code to the J-PARC synchrotrons. The results of benchmarking are also reported.

Flame Imaging Technology Based on 64-Pixel Area Array Sensor.

High-resolution flame temperature images are essential indicators for evaluating combustion conditions. Tunable diode laser absorption spectroscopy (TDLAS) is an effective combustion diagnostic method. In actual engineering, due to the limitation of line-of-sight (LOS) measurement, TDLAS technology has the problems of small data volume and low dimensionality in measuring combustion fields, which seriously limits the development of TDLAS in combustion diagnosis. This article demonstrates a TDLAS imaging method based on a 64-pixel area array sensor to reconstruct the two-dimensional temperature field of the flame. This paper verifies the robustness of the Algebraic Reconstruction Technique (ART) algorithm through numerical simulation and studies the effects of temperature, concentration, and pressure on the second harmonic intensity based on the HITRAN database. The two-dimensional temperature field of the flame was reconstructed, and reconstruction accuracy was verified using thermocouples. The maximum relative error was 3.71%. The TDLAS detection system based on a 64-pixel area array sensor provides a way to develop high-precision, high-complexity flame temperature measurement technology.

Reconstruction Algorithm Optimization Based on Multi-Iteration Adaptive Regularity for Laser Absorption Spectroscopy Tomography

Laser absorption spectroscopy tomography is an effective combustion diagnostic method for obtaining simultaneous two-dimensional distribution measurements of temperature and gas molar concentrations. For the reconstruction process of complex combustion flames, a new algorithm named ‘multi-iterative adaptive optimization regularization’ (MIARO) is proposed. This algorithm is a further development of another algorithm known as the ‘modified adaptive algebraic reconstruction technique’ (MAART) with the improvement of the initial value and adaptive regularization parameter selections. In MIARO, the problem of the MAART’s initial value sensitivity is compensated for, and in addition, reconstruction parameters are also introduced into the regularization so that both the quality of reconstruction and the convergence of regularization are guaranteed. In butane burner experiments, an average relative error of 1.82% was achieved with MIARO, compared to 2.44% with MAART, which is a significant reduction of 25.1%. The simulation and experimental results clearly demonstrate that the MIARO algorithm can be used to reconstruct dynamic combustion fields and eliminate boundary artifacts with improved measurement accuracy and robustness.

Convergence of the Multiplicative Algebraic Reconstruction Technique for the Inconsistent System of Equations

Convergence of the Multiplicative Algebraic Reconstruction Technique for the Inconsistent System of Equations

Preliminary commissioning of a prototype solid tank optical CT scanner for 3D radiation dosimetry

Optical computed tomography (CT) is one of the leading modalities for imaging gel dosimeters. In previous research, it was shown that a design could significantly reduce the volume of the refractive index baths that are commonly found in optical CT systems. The proposed scanner has been manufactured and is in process of being commissioned. The rays refract through the system and their paths are estimated using a ray-tracing simulator. Reconstruction is preformed through algebraic reconstruction technique and iterated using the FISTA-TV algorithm. A Sylgard®184 edge phantom was created to commission the scanner’s spatial resolution. The scanner is capable of a 0.929 mm−1 spatial resolution, although the spatial resolution is highly dependent on the number of iterations, and method of processing the edge spread function.

Study of γ-Ray Spectrum Measurement Analysis Algorithm of Radioactive Solid Waste Steel Boxes

Abstract In accordance with safety requirements for the near-surface disposal of low and medium-level radioactive solid waste, accurate identification and measurement of radionuclide types and activities within steel boxes containing such waste are necessary. Conventional sampling techniques are impractical due to nonuniform internal filling and radioactive distribution in the steel boxes used for storage. Nondestructive measurement analysis techniques offer significant advantages by providing comprehensive measurements without causing damage to the steel boxes or generating secondary waste. Therefore, nondestructive techniques are widely applicable and superior to chemical analysis methods. This study presents an algorithm for analyzing γ-ray spectrum measurements of radioactive solid waste steel boxes by combining the traditional computed tomography (CT) principle with a discrete treatment approach. The progressive split voxel measurement method is utilized to discretely handle the radioactive solid waste steel boxes during the measurement and calculation process while considering the impact of voxel interactions on detection efficiency. A detection efficiency calibration model is established using Monte Carlo (MC) simulation in conjunction with the algebraic reconstruction technique (ART). Additionally, an inversion correction of the efficiency for the physically coincident portion of the detected voxel volume is performed during the measurement process. The proposed algorithm is initially applied to the analysis platform of steel boxes that store FA-IV-type radioactive solid waste. The algorithm's performance is further investigated and validated using standard radioactive sources with known activity levels. The results indicate that the relative deviation between the reconstruction results and the nominal values of radioactive activities in the steel boxes is less than 30%. These findings align with the expected results and satisfy the measurement analysis and warehousing processing requirements for waste generated from the decommissioning of China's 101 nuclear reactor. The proposed algorithm holds great potential for widespread application in related detection work.

Uniformly sampled polar and cylindrical grid approach for 2D, 3D image reconstruction using algebraic algorithm

Image reconstruction by Algebraic Methods (AM) outperforms the transform methods in situations where the data collection procedure is constrained by time, space, and radiation dose. AM algorithms can also be applied for the cases where these constraints are not present but their high computational and storage requirement prohibit their actual breakthrough in such cases. In the present work, we propose a novel Uniformly Sampled Polar/Cylindrical Grid (USPG/USCG) discretization scheme to reduce the computational and storage burden of algebraic methods. The symmetries of USPG/USCG are utilized to speed up the calculations of the projection coefficients. In addition, we also offer an efficient approach for USPG to Cartesian Grid (CG) transformation for the visualization. The Multiplicative Algebraic Reconstruction Technique (MART) has been used to process the projections data in order to determine the field function of the suggested grids. We first use cyber phantoms of various shapes, sizes and densities to test the USPG/USCG-based MART algorithm. Experimental projections data of a frog and Cu-Lump have been further exercised to validate the proposed approach. A variety of image quality measures have been evaluated to check the accuracy of the reconstruction. Results indicate that the current strategies speed up (when compared to CG-based algorithms) the reconstruction process by a factor of 2.5 and reduce the memory requirement by the factor p, the number of projections used in the reconstruction.

Tomographic optical emission spectroscopy of an atmospheric pressure plasma jet and surface ionization waves on planar and structured surfaces

In this paper, an approach for 3D plasma structure diagnostics using tomographic optical emission spectroscopy (Tomo-OES) of a nanosecond pulsed atmospheric pressure plasma jet (APPJ) is presented. In contrast to the well-known Abel inversion, Tomo-OES does not require cylindrical symmetry to recover 3D distributions of plasma light emission. Instead, many 2D angular projections are measured with intensified cameras and the multiplicative algebraic reconstruction technique is used to recover the 3D distribution of light emission. This approach solves the line-of-sight integration problem inherent to optical diagnostics, allowing recovery of localized OES information within the plasma that can be used to better infer plasma parameters within complex plasma structures. Here, Tomo-OES was applied to investigate an APPJ operated with helium in ambient air and impinging on planar and structured dielectric surfaces. Surface charging caused the guided streamer from the APPJ to transition to a surface ionization wave (SIW) that propagated along the surface. The SIW experienced variable geometrical and electrical material properties as it propagated, leading to 3D configurations that were non-symmetric and spatially complex. Light emission from He, N, and N2 were imaged at ten angular projections and the respective time-resolved 3D emission distributions in the plasma were then reconstructed. The spatial resolution of each tomographic reconstruction was 7.4 µm and the temporal resolution was 5 ns, sufficient to observe the guided streamer and the effects of the structured surface on the SIW. Emission from He showed the core of the jet and emission from N and N2 indicated effects of entrainment of ambient air. Penning ionization of N2 created a ring or outer layer of N that spatially converged to form the ‘plasma bullet’ or spatially diverged across a surface as part of a SIW. The SIW entered trenches of size 150 µm, leading to decreases in plasma light emission in regions above the trenches. The plasma light emission was higher in some regions with trenches, possibly due to effects of field enhancement.

High‐pressure gas temperature sensing for exit plane of aero‐engine combustor using tunable diode laser absorption spectroscopy

AbstractWe have developed a sensor for the temperature measurement in the test section after the combustion chamber of an aero engine model by using direct absorption spectroscopy. Five distributed feedback diode lasers at near 1392, 1393, 1339, 1343, and 1469 nm are utilized as the light sources to detect H2O absorptions to improve the precision of temperature measurement combining with the Boltzmann plot method and the polynomial‐based spectral fitting model. The sensor shows a good performance in terms of its temperature measurement accuracy under high temperature of 673–1373 K and high pressure of 100–600 kPa condition in a tube furnace, which was lower than 4%. Moreover, three‐dimensional temperature distributions have been reconstructed via applying algebraic reconstruction technique at the test section after the combustion chamber of an aero engine model. The single‐point position temperature extracted from the algebraic reconstruction technique agrees well with that measured from the coherent anti‐stokes Raman scattering technique, where the relative error is within 5%. All the above results prove the reliability of our developed temperature sensor.

Dynamic imaging of three-dimensional temperature field via three-directional wavelength modulated lateral shearing interferometry

A three-directional wavelength modulated lateral shearing interference system was proposed for the dynamic three-dimensional visualization of a temperature field. The laser emitted from a distributed feedback (DFB) laser was divided into three beams by a fiber beam splitter. The beams were spatially expanded and passed through the flame in three directions of 0°, 120° and 240°, respectively. The three interferograms formed by reflections from the front and back surfaces of the parallel glass plates were spatially converged into the lens of a high-speed camera. Multiple plane mirrors were utilized to reflect the beams. The size of the region of interest (ROI) was −20 ∼ 20 mm in both x and z directions and 5 ∼ 30 mm in y direction, with a spatial resolution of 200 μm in all directions. A three-dimensional sensitivity matrix was modeled, and the simultaneous algebraic reconstruction technique (SART) was used for layer-by-layer imaging to achieve three-dimensional flame monitoring. Numerical simulations verified the effectiveness of the algorithm qualitatively and quantitatively. In experiments, the temperature distributions of four cases of flames, namely, steady diffused flame, partially blocked diffused flame, dynamic acoustically excited flame and the flame after ignition, were reconstructed at 1k frames per second (fps). The flame structures and temporal variations of temperature distributions were clearly visualized, demonstrating the ability of the system in fast monitoring of three-dimensional dynamic temperature fields.

Study on the Location Determination of Building Fire Points Based on Acoustic CT Temperature Measurement

Rapid perception of the location of the fire point is crucial to building fire emergency response in the process of building fire emergency response, which can help firefighters direct fire-fighting operations, effectively control fire sources, and provide strong evidence for the analysis and investigation of fire causes. This paper uses acoustic CT temperature measurement technology to determine the fire source location of a building fire and verifies its validity and applicability as follows: we construct various fire point numerical models based on the fire dynamics simulator (FDS) and obtain temperature data at different times; neural network means were used to obtain the time-of-flight (TOF) of an acoustic wave traveling; the large ill-conditioned matrix equation of acoustic flight under different meshing schemes was constructed and solved based on the simultaneous algebraic reconstruction technique (SART) and least squares QR-decomposition (LSQR), and then reconstruction temperature data under each scheme were obtained. Through the error analysis, the reconstruction effect of each reconstruction scheme is evaluated, and then the applicability of the location coordinate determination of the fire point is analyzed. The results show that the determination of the fire location under the conditions of various fire points in the building space can be realized by acoustic CT temperature measurement technology.

Volume integral model for algebraic image reconstruction and computed tomography

Industrial computed tomography (CT) has seen widespread adoption as an inspection technique due to its ability to resolve small defects and perform high-resolution measurements on complex structures. The reconstruction of CT data is usually performed using filtered back-projection (FBP) methods, such as the Feldkamp-Davis-Kress (FDK) method, and are selected as they offer a good compromise between reconstruction time and quality. More recently, iterative reconstruction algorithms have seen a resurgence in research interest as computing power has increased. Iterative reconstruction algorithms, such as the algebraic reconstruction technique (ART), use a reconstruction approach based on linear algebra to determine voxel attenuation coefficients based on the measured attenuation of the sample at the detector and calculation of the ray paths traversing the voxel grid. This offers a more precise model for CT reconstruction but at the cost of computational complexity and reconstruction time. Existing ART implementations are based on the 2D weighting models of the binary integral method (BIM), line integral method (LIM) and area integral method (AIM). For full 3D reconstruction, BIM and LIM only offer approximations leading to numerical inaccuracies. AIM for 2D reconstruction is mathematically exact but considers the divergent nature of a fan beam for 2D only. For a full 3D volumetric reconstruction, the X-ray cone beam is divergent in all directions and therefore AIM cannot be applied in its current form. A novel voxel weighting method for 3D volumetric image reconstruction using ART and providing a mathematically exact fractional volume weighting is introduced in this paper and referred to as the volume integral method (VIM). A set of algorithms is provided based on computer graphics techniques to determine ray/voxel intersections with volume reconstruction computed based on the divergence theorem. A set of experimental configurations is developed to provide a comparison against existing methods and conclusions are provided. Optimisation is achieved through graphic acceleration.

Joint Bi-Modal Tomographic Reconstruction from Observations with Missing Data

A method for tomographic reconstruction of bi-modal data sets using cross modal regularization was developed. The method constrains the Simultaneous Algebraic Reconstruction Technique by using clustering-based segmented images and quality controlled fused images, to jointly regularize the reconstruction of structures imaged with different methods. The joint regularized reconstruction method was tested using a synthetic X-Ray and neutron data set with a mix of attenuation driven data starvation. Assuming consistent material boundaries in the different imaging modalities, it was shown that improvements in terms of the Feature Similarity Index Measure are made compared to a traditional SART-TV reconstruction. UK Ministry of Defence ©Crown Owned Copyright 2023/AWE