Search NASA⌕ Search

SEARCH · Search NASA

Results for “radon transform”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

14 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Building bulk geometry from the tensor Radon transform

Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS 3 /CFT 2 . We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A Linear-Complexity Tensor Butterfly Algorithm for Compressing High-Dimensional Oscillatory Integral Operators

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a d-dimensional (d > 1) integral operator discretized into a 2d-mode tensor with n2d entries, the overall CPU time and memory requirement scale as O(nd), in stark contrast to the O(nd log n) complexity of existing matrix algorithms such as matrix butterfly algorithms and fast Fourier transforms (FFTs), where n is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents problems of scale over 512× larger than that existing butterfly algorithms can handle, with the same amount of computation resources. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algebraic matrix algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and 30× memory reduction compared with existing ones. Moreover, the tensor butterfly algorithm also permits O(nd)-complexity FFTs and Radon transforms up to d = 6 dimensions.

Kielstra, P Michael↗
DOE OSTI2020

An Experimental Feasibility Study on Applying Neutron Tomography to Encapsulated Spent Nuclear Fuel - 20050

Visual inspection makes easier to ensure the integrity and safety of spent nuclear fuel (SNF) than any classical techniques. Various classical techniques have been applied but there are no reliable methods to qualitatively and quantitatively verify spent fuel in dry storage. Thus, the present authors have developed the prototype safeguards apparatus for dry storage employing the array of He-4 gas scintillation detectors (S670E, Arktis Radiation Detectors Ltd., Switzerland), newly designed to simultaneously measure thermal and fast neutrons without any moderators. The S670E detector has a cylindrical shape with a diameter of 52 mm and active length of 600 mm (total length: 875 mm). The detector is filled by He-4 gas with an approximate pressure of 180 bar for fast neutron detection, and its inner wall is coated by Li-6 for thermal neutron detection. The scintillation lights generated via Li-6 nuclear reaction and elastic scattering are collected by 24 SiPMs linearly paired at the center of the detector. The detector delivers a TTL (Transistor-Transistor Logic) output for pulse readout and UART (Universal Asynchronous Receiver Transmitter) for device control. In order to assess feasibility of the apparatus, an experimental system has been designed, built, and optimized via computational studies. Cf-252 neutron sources and linearly arrayed detectors, working as a single detector, were occupied for this study due to the difficulties in working with SNF. The laboratory scale cask (diameter: 0.67 m, height: 1.5 m), minimized by a factor of 10 compared to the actual thickness of a commercial TN-32 cask, was also manufactured. The detector array was designed to rotate the lab-scale cask and obtain 36 image profiles at every 10 degrees. All profiles were aligned in single frame image called a sinogram, and the cross-sectional image was then fabricated by the inverse radon transform algorithm. These experiments have been repeated with different configurations and numbers of sources. Some gamma-ray sources were also measured with neutron sources in order to distinguish between neutron and gamma-ray pulses. Basically, a He-4 detector is designed to run on Linux OS so it is difficult to directly apply to Windows-based equipment widely used in S. Korea. Therefore, a new data acquisition board working on Windows OS was designed and built. The board mainly consists of FPGA (Field Programmable Gate Array) and SoC (System on Chip) for TTL pulse readout, sorting measured data, and transferring data to a user interface. In conclusion, the tomographic system at lab-scale has shown considerable potential to detect a partial or gross defect of encapsulated assemblies in dry storage. Next steps of this study will be to 1) repeatedly carry out experiments to demonstrate scientific reliability and validity, and 2) numerically integrate signals with weight factors to enhance the image quality since the suggested system based on passive interrogation method requires longer measurement time. Finally, the system will apply to a commercial dry storage phased out soon in S. Korea. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2021

Quantitative imaging and automated fuel pin identification for passive gamma emission tomography

Compliance of member States to the Treaty on the Non-Proliferation of Nuclear Weapons is monitored through nuclear safeguards. The Passive Gamma Emission Tomography (PGET) system is a novel instrument developed within the framework of the International Atomic Energy Agency (IAEA) project JNT 1510, which included the European Commission, Finland, Hungary and Sweden. The PGET is used for the verification of spent nuclear fuel stored in water pools. Advanced image reconstruction techniques are crucial for obtaining high-quality cross-sectional images of the spent-fuel bundle to allow inspectors of the IAEA to monitor nuclear material and promptly identify its diversion. In this work, we have developed a software suite to accurately reconstruct the spent-fuel cross sectional image, automatically identify present fuel rods, and estimate their activity. Unique image reconstruction challenges are posed by the measurement of spent fuel, due to its high activity and the self-attenuation. While the former is mitigated by detector physical collimation, we implemented a linear forward model to model the detector responses to the fuel rods inside the PGET, to account for the latter. The image reconstruction is performed by solving a regularized linear inverse problem using the fast-iterative shrinkage-thresholding algorithm. We have also implemented the traditional filtered back projection (FBP) method based on the inverse Radon transform for comparison and applied both methods to reconstruct images of simulated mockup fuel assemblies. Higher image resolution and fewer reconstruction artifacts were obtained with the inverse-problem approach, with the mean-square-error reduced by 50%, and the structural-similarity improved by 200%. We then used a convolutional neural network (CNN) to automatically identify the bundle type and extract the pin locations from the images; the estimated activity levels finally being compared with the ground truth. The proposed computational methods accurately estimated the activity levels of the present pins, with an associated uncertainty of approximately 5%.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Accurate real space iterative reconstruction (RESIRE) algorithm for tomography

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at https://zenodo.org/record/7273314.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Real space iterative reconstruction for vector tomography (RESIRE-V)

Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method. To make the algorithm accessible to a broad user community, we have made our RESIRE-V MATLAB source codes and the data freely available at https://github.com/minhpham0309/RESIRE-V.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Lorentzian OPE inversion formula: A geometric perspective

We give a new perspective on the Lorentzian operator product expansion inversion formula [S. Caron-Huot, Analyticity in spin in conformal theories, .; D. Simmons-Duffin, D. Stanford, and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, .], building on [P. Agarwal , companion paper, Embedding space approach to Lorentzian CFT amplitudes and causal spherical functions, .]. We introduce an “auxiliary” fourpoint function that can be related to the traditionally defined ones via a Radon transform. The Mellin amplitudes associated with this auxiliary function can be shown to be equivalent to the conventional partial wave amplitudes. This has the intuitive geometrical meaning of a generalization of the projection-slice theorem. Published by the American Physical Society 2025

Agarwal, Pulkit (ORCID:0000000346581691)↗
DOE OSTI2025

Experimental study of multiple-orientation muon tomography with image optimization in sparse data environments

Due to the high penetrating power of cosmic-ray muons, they can be used to probe very thick and dense objects. As muons are charged particles, they can be tracked by ionization detectors, determining the position and direction of the muons. With detectors on either side of an object to measure particle direction change, scattering information within the object can be found. This can be used to produce a scattering-intensity image within the object related to density and atomic number. Such imaging is typically performed with a single detector-object orientation, taking advantage of the more intense downward flux of muons, producing planar imaging with some depth-of-field information in the third dimension. Several simulation studies were published with multiorientation tomography, which can form a three-dimensional representation faster than a single-orientation view. In this study, experimental muon-scatter-based tomography was performed using a concrete filled steel drum with several different metal wedges inside, with the drum between detector planes. Data were collected from different detector-object orientations by rotating the steel drum. The data collected from each orientation were combined using two different tomographic methods. A traditional inverse Radon transform approach used for computed tomography and a combination of multiple depth-of-field reconstructions were applied to the data. As cosmic-ray muon flux imaging is rate limited, the imaging techniques were compared for sparse data. Using the combined depth-of-field reconstruction technique, fewer detector-object orientations were needed to reconstruct images that could be used to differentiate the metal wedges.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

First experimental study of multiple orientation muon tomography, with image optimization in sparse data environments

Due to the high penetrating power of cosmic ray muons, they can be used to probe very thick and dense objects. As charged particles, they can be tracked by ionization detectors, determining the position and direction of the muons. With detectors on either side of an object, particle direction changes can be used to extract scattering information within an object. This can be used to produce a scattering intensity image within the object related to density and atomic number. Such imaging is typically performed with a single detector-object orientation, taking advantage of the more intense downward flux of muons, producing planar imaging with some depth-of-field information in the third dimension. Several simulation studies have been published with multi-orientation tomography, which can form a three-dimensional representation faster than a single orientation view. In this work we present the first experimental multiple orientation muon tomography study. Experimental muon-scatter based tomography was performed using a concrete filled steel drum with several different metal wedges inside, between detector planes. Data was collected from different detector-object orientations by rotating the steel drum. The data collected from each orientation were then combined using two different tomographic methods. Results showed that using a combination of multiple depth-of-field reconstructions, rather than a traditional inverse Radon transform approach used for CT, resulted in more useful images for sparser data. As cosmic ray muon flux imaging is rate limited, the imaging techniques were compared for sparse data. Using the combined depth-of-field reconstruction technique, fewer detector-object orientations were needed to reconstruct images that could be used to differentiate the metal wedge compositions.

Applied Physics (physics.app-ph)↗
DOE OSTI2021

Boundary detection evaluation

Illustrative embodiments are directed to a method and apparatus for evaluating boundary detection in an image. A processed image is received, wherein a detected boundary of an image of an object is identified in the processed image. A Radon transform is applied to the processed image for a plurality of angles to form a processed image histogram corresponding to the detected boundary for each of the plurality of angles. The processed image histogram for each of the plurality of angles and a corresponding ground truth histogram for each of the plurality of angles is normalized to provide a normalized processed image histogram and a normalized ground truth histogram for each of the plurality of angles, wherein the ground truth histogram corresponds to a ground truth boundary of the object for a corresponding angle. An indication of the edges of the normalized processed image histogram for each of the plurality of angles is plotted to form a boundary detection evaluation visualization.

Wantuch, Andrew C.↗
DOE OSTI2023

Computed axial lithography optimization system

A system for determining a light intensity field for use in manufacturing a 3D object from a volume of material. The system receives a 3D specification of a 3D geometry for the 3D object that specifies voxels within the volume that contain material that is to be part of the 3D object. The system employs a cost function for effectiveness of a light intensity field in manufacturing the 3D object. The cost function may be an adjoint of an Attenuated Radon Transform that models an energy dose that each voxel would receive during manufacture of the 3D object using the light intensity field. The system applies an optimization technique that employs the cost function to generate a measure of the effectiveness of possible light intensity fields and outputs an indication of a light intensity field that will be effective in manufacturing the 3D object.

Shusteff, Maxim↗
DOE OSTI2024

Boundary detection evaluation

Illustrative embodiments are directed to a method and apparatus for evaluating boundary detection in an image. A processed image is received, wherein a detected boundary of an image of an object is identified in the processed image. A Radon transform is applied to the processed image for a plurality of angles to form a processed image histogram corresponding to the detected boundary for each of the plurality of angles. The processed image histogram for each of the plurality of angles and a corresponding ground truth histogram for each of the plurality of angles is normalized to provide a normalized processed image histogram and a normalized ground truth histogram for each of the plurality of angles, wherein the ground truth histogram corresponds to a ground truth boundary of the object for a corresponding angle. An indication of the edges of the normalized processed image histogram for each of the plurality of angles is plotted to form a boundary detection evaluation visualization.

Wantuch, Andrew C.↗
DOE OSTI2024

tomoCAM : fast model-based iterative reconstruction via GPU acceleration and non-uniform fast Fourier transforms

X-ray-based computed tomography is a well established technique for determining the three-dimensional structure of an object from its two-dimensional projections. In the past few decades, there have been significant advancements in the brightness and detector technology of tomography instruments at synchrotron sources. These advancements have led to the emergence of new observations and discoveries, with improved capabilities such as faster frame rates, larger fields of view, higher resolution and higher dimensionality. These advancements have enabled the material science community to expand the scope of tomographic measurements towards increasingly in situ and in operando measurements. In these new experiments, samples can be rapidly evolving, have complex geometries and restrictions on the field of view, limiting the number of projections that can be collected. In such cases, standard filtered back-projection often results in poor quality reconstructions. Iterative reconstruction algorithms, such as model-based iterative reconstructions (MBIR), have demonstrated considerable success in producing high-quality reconstructions under such restrictions, but typically require high-performance computing resources with hundreds of compute nodes to solve the problem in a reasonable time. Here, tomoCAM , is introduced, a new GPU-accelerated implementation of model-based iterative reconstruction that leverages non-uniform fast Fourier transforms to efficiently compute Radon and back-projection operators and asynchronous memory transfers to maximize the throughput to the GPU memory. The resulting code is significantly faster than traditional MBIR codes and delivers the reconstructive improvement offered by MBIR with affordable computing time and resources. tomoCAM has a Python front-end, allowing access from Jupyter -based frameworks, providing straightforward integration into existing workflows at synchrotron facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗