scholarly journals A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling

2021 ◽  
Vol 7 (11) ◽  
pp. 246
Author(s):  
Axel Henningsson ◽  
Stephen A. Hall
Keyword(s):  
Tomographic Reconstruction ◽  
Reconstruction Algorithm ◽  
Projection Data ◽  
Granular System ◽  
Mathematical Framework ◽  
Discrete Elements ◽  
Full Field ◽  
Attenuation Field ◽  
4D Reconstruction ◽  
Selection Of

A mathematical framework and accompanying numerical algorithm exploiting the continuity equation for 4D reconstruction of spatiotemporal attenuation fields from multi-angle full-field transmission measurements is presented. The algorithm is geared towards rotation-free dynamic multi-beam X-ray tomography measurements, for which angular information is sparse but the temporal information is rich. 3D attenuation maps are recovered by propagating an initial discretized density volume in time according to the advection equations using the Finite Volumes method with a total variation diminishing monotonic upstream-centered scheme (TVDMUSCL). The benefits and limitations of the algorithm are explored using dynamic granular system phantoms modelled via discrete elements and projected by an analytical ray model independent from the numerical ray model used in the reconstruction scheme. Three phantom scenarios of increasing complexity are presented and it is found that projections from only a few (unknowns:equations > 10) angles can be sufficient for characterisation of the 3D attenuation field evolution in time. It is shown that the artificial velocity field produced by the algorithm sub-iteration, which is used to propagate the attenuation field, can to some extent approximate the true kinematics of the system. Furthermore, it is found that the selection of a temporal interpolation scheme for projection data can have a significant impact on error build up in the reconstructed attenuation field.

Three Dimensional Reconstruction From Limited Projection Data Using a Novel MART Algorithm

1999 ◽  
Author(s):  
Debasish Mishra ◽  
K. Muralidhar ◽  
P. Munshi
Keyword(s):  
Fluid Layer ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
Reconstruction Algorithm ◽  
Projection Data ◽  
Three Dimensional Reconstruction ◽  
Time Requirement ◽  
Dimensional Reconstruction ◽  
Heated Fluid ◽  
Relaxation Factors

Abstract The present work is concerned with the development of a robust three dimensional reconstruction algorithm for applications involving tomography. In an earlier study it was shown that among the ART family of algorithms the multiplicative algebraic reconstruction algorithm (MART) was the most appropriate for tomographic reconstruction. In the present work, the MART algorithm has been extended so that (a) its performance is acceptable over a wider range of relaxation factors, (b) the time requirement for convergence to a solution is lower and (c) its performance is less sensitive to noise in the projection data. Two applications have been considered for evaluating the proposed algorithms namely a circular region with holes and experimental data recorded in a differentially heated fluid layer using an interferometer. The algorithms proposed are seen to be clearly an improvement over those presently available.

scholarly journals Dense U-Net for Limited Angle Tomography of Sound Pressure Fields

2021 ◽  
Vol 11 (10) ◽  
pp. 4570
Author(s):  
Oliver Rothkamm ◽  
Johannes Gürtler ◽  
Jürgen Czarske ◽  
Robert Kuschmierz
Keyword(s):  
Measurement Errors ◽  
Sound Pressure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Projection Data ◽  
Quantitative Measurements ◽  
Pressure Fields ◽  
The Neural Network ◽  
Bias Flow ◽  
3D Information

Tomographic reconstruction allows for the recovery of 3D information from 2D projection data. This commonly requires a full angular scan of the specimen. Angular restrictions that exist, especially in technical processes, result in reconstruction artifacts and unknown systematic measurement errors. We investigate the use of neural networks for extrapolating the missing projection data from holographic sound pressure measurements. A bias flow liner was studied for active sound dampening in aviation. We employed a dense U-Net trained on synthetic data and compared reconstructions of simulated and measured data with and without extrapolation. In both cases, the neural network based approach decreases the mean and maximum measurement deviations by a factor of two. These findings can enable quantitative measurements in other applications suffering from limited angular access as well.

scholarly journals Correction for the Partial Volume Effects (PVE) in Nuclear Medicine Imaging: A Post-Reconstruction Analytic Method

2021 ◽  
Vol 11 (14) ◽  
pp. 6460
Author(s):  
Fabio Di Martino ◽  
Patrizio Barca ◽  
Eleonora Bortoli ◽  
Alessia Giuliano ◽  
Duccio Volterrani
Keyword(s):  
Nuclear Medicine ◽  
Imaging System ◽  
Tomographic Reconstruction ◽  
Mathematical Expression ◽  
Reconstruction Algorithm ◽  
Volume Effect ◽  
Nuclear Medicine Imaging ◽  
Theoretical Derivation ◽  
Reconstruction Process ◽  
Partial Volume

Quantitative analyses in nuclear medicine are increasingly used, both for diagnostic and therapeutic purposes. The Partial Volume Effect (PVE) is the most important factor of loss of quantification in Nuclear Medicine, especially for evaluation in Region of Interest (ROI) smaller than the Full Width at Half Maximum (FWHM) of the PSF. The aim of this work is to present a new approach for the correction of PVE, using a post-reconstruction process starting from a mathematical expression, which only requires the knowledge of the FWHM of the final PSF of the imaging system used. After the presentation of the theoretical derivation, the experimental evaluation of this method is performed using a PET/CT hybrid system and acquiring the IEC NEMA phantom with six spherical “hot” ROIs (with diameters of 10, 13, 17, 22, 28, and 37 mm) and a homogeneous “colder” background. In order to evaluate the recovery of quantitative data, the effect of statistical noise (different acquisition times), tomographic reconstruction algorithm with and without time-of-flight (TOF) and different signal-to-background activity concentration ratio (3:1 and 10:1) was studied. The application of the corrective method allows recovering the loss of quantification due to PVE for all sizes of spheres acquired, with a final accuracy less than 17%, for lesion dimensions larger than two FWHM and for acquisition times equal to or greater than two minutes.

scholarly journals Shearlet-based regularized reconstruction in region-of-interest computed tomography

2018 ◽  
Vol 13 (4) ◽  
pp. 34
Author(s):  
T.A. Bubba ◽  
D. Labate ◽  
G. Zanghirati ◽  
S. Bonettini
Keyword(s):  
Optimization Problem ◽  
Ad Hoc ◽  
Iterative Scheme ◽  
Tomographic Reconstruction ◽  
Region Of Interest ◽  
Projection Data ◽  
Reconstruction Problem ◽  
Convex Optimization Problem ◽  
Scanning Time ◽  
Novel Approach

Region of interest (ROI) tomography has gained increasing attention in recent years due to its potential to reducing radiation exposure and shortening the scanning time. However, tomographic reconstruction from ROI-focused illumination involves truncated projection data and typically results in higher numerical instability even when the reconstruction problem has unique solution. To address this problem, bothad hocanalytic formulas and iterative numerical schemes have been proposed in the literature. In this paper, we introduce a novel approach for ROI tomographic reconstruction, formulated as a convex optimization problem with a regularized term based on shearlets. Our numerical implementation consists of an iterative scheme based on the scaled gradient projection method and it is tested in the context of fan-beam CT. Our results show that our approach is essentially insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.

Ultra-limited-angle CT image reconstruction algorithm based on reweighting and edge-preserving

2022 ◽  
pp. 1-13
Author(s):  
Lei Shi ◽  
Gangrong Qu ◽  
Yunsong Zhao
Keyword(s):  
Image Reconstruction ◽  
Condition Number ◽  
Reconstruction Algorithm ◽  
Projection Data ◽  
Ct Image ◽  
Reconstruction Algorithms ◽  
Edge Preserving ◽  
Image Reconstruction Algorithm ◽  
Ct Image Reconstruction ◽  
Limited Angle

BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π 2 is severely ill-posed. Due to the considerably large condition number of a linear system for image reconstruction, it is extremely challenging to generate a valid reconstructed image by traditional iterative reconstruction algorithms. OBJECTIVE: To develop and test a valid ultra-limited-angle CT image reconstruction algorithm. METHODS: We propose a new optimized reconstruction model and Reweighted Alternating Edge-preserving Diffusion and Smoothing algorithm in which a reweighted method of improving the condition number is incorporated into the idea of AEDS image reconstruction algorithm. The AEDS algorithm utilizes the property of image sparsity to improve partially the results. In experiments, the different algorithms (the Pre-Landweber, AEDS algorithms and our algorithm) are used to reconstruct the Shepp-Logan phantom from the simulated projection data with noises and the flat object with a large ratio between length and width from the real projection data. PSNR and SSIM are used as the quantitative indices to evaluate quality of reconstructed images. RESULTS: Experiment results showed that for simulated projection data, our algorithm improves PSNR and SSIM from 22.46db to 39.38db and from 0.71 to 0.96, respectively. For real projection data, our algorithm yields the highest PSNR and SSIM of 30.89db and 0.88, which obtains a valid reconstructed result. CONCLUSIONS: Our algorithm successfully combines the merits of several image processing and reconstruction algorithms. Thus, our new algorithm outperforms significantly other two algorithms and is valid for ultra-limited-angle CT image reconstruction.

A new weighting scheme for arc based circle cone-beam CT reconstruction

2021 ◽  
pp. 1-19
Author(s):  
Wei Wang ◽  
Xiang-Gen Xia ◽  
Chuanjiang He ◽  
Zemin Ren ◽  
Jian Lu
Keyword(s):  
Characteristic Function ◽  
Weighting Function ◽  
Cone Beam Ct ◽  
Reconstruction Algorithm ◽  
Cone Beam ◽  
Characteristic Functions ◽  
Projection Data ◽  
Ct Reconstruction ◽  
Scanning Angle ◽  
Beam Geometry

In this paper, we present an arc based fan-beam computed tomography (CT) reconstruction algorithm by applying Katsevich’s helical CT image reconstruction formula to 2D fan-beam CT scanning data. Specifically, we propose a new weighting function to deal with the redundant data. Our weighting function ϖ ( x _ , λ ) is an average of two characteristic functions, where each characteristic function indicates whether the projection data of the scanning angle contributes to the intensity of the pixel x _ . In fact, for every pixel x _ , our method uses the projection data of two scanning angle intervals to reconstruct its intensity, where one interval contains the starting angle and another contains the end angle. Each interval corresponds to a characteristic function. By extending the fan-beam algorithm to the circle cone-beam geometry, we also obtain a new circle cone-beam CT reconstruction algorithm. To verify the effectiveness of our method, the simulated experiments are performed for 2D fan-beam geometry with straight line detectors and 3D circle cone-beam geometry with flat-plan detectors, where the simulated sinograms are generated by the open-source software “ASTRA toolbox.” We compare our method with the other existing algorithms. Our experimental results show that our new method yields the lowest root-mean-square-error (RMSE) and the highest structural-similarity (SSIM) for both reconstructed 2D and 3D fan-beam CT images.

scholarly journals Parallel approach to tomographic reconstruction algorithm using a Nvidia GPU

2019 ◽  
Author(s):  
Tomás Antonio Valencia Pérez ◽  
Javier Miguel Hernández López ◽  
Eduardo Moreno Barbosa ◽  
Mario Iván Martínez Hernández ◽  
Guillermo Tejeda Muñoz ◽  
...  
Keyword(s):  
Tomographic Reconstruction ◽  
Reconstruction Algorithm ◽  
Nvidia Gpu

Recent Development of Cone-Beam X-Ray Microtomography at Sunyab

1997 ◽  
Vol 3 (S2) ◽  
pp. 1125-1126
Author(s):  
S.J. Pan ◽  
A. Shih ◽  
W.S. Liou ◽  
M.S. Park ◽  
G. Wang ◽  
...  
Keyword(s):  
Dynamic Range ◽  
Imaging System ◽  
Tomographic Reconstruction ◽  
Ccd Camera ◽  
Test Sample ◽  
Glass Beads ◽  
Cone Beam ◽  
Projection Data ◽  
X Ray ◽  
Cooled Ccd

An experimental X-ray cone-beam microtomographic imaging system utilizing a generalized Feldkamp reconstruction algorithm has been developed in our laboratory. This microtomographic imaging system consists of a conventional dental X-ray source (Aztech 65, Boulder, CO), a sample position and rotation stage, an X-ray scintillation phosphor screen, and a high resolution slow scan cooled CCD camera (Kodak KAF 1400). A generalized Feldkamp cone-beam algorithm was used to perform tomographic reconstruction from cone-beam projection data. This algorithm was developed for various hardware configuration to perform reconstruction of spherical, rod-shaped and plate-like specimen.A test sample consists of 8 glass beads (approx. 800μm in diameter) dispersed in an epoxy-filled #0 gelatin capsule. One hundred X-ray projection images were captured equal angularly (at 3.6 degree spacing) by the cooled CCD camera at a of 1317×967 (17×17mm2) pixels with 12-bit dynamic range. Figure 1 shows a 3D isosurface rendering of the test sample. The eight glass beads and trapped air bubbles (arrows) in the epoxy resin (e) are clearly visible.

scholarly journals Simulation studies on the tomographic reconstruction of the equatorial and low-latitude ionosphere in the context of the Indian tomography experiment: CRABEX

2004 ◽  
Vol 22 (10) ◽  
pp. 3445-3460 ◽  
Author(s):  
S. V. Thampi ◽  
T. K. Pant ◽  
S. Ravindran ◽  
C. V. Devasia ◽  
R. Sridharan
Keyword(s):  
Tomographic Reconstruction ◽  
Reconstruction Algorithm ◽  
Equatorial Region ◽  
Spatial And Temporal Variability ◽  
Inversion Algorithm ◽  
Low Latitude ◽  
Density Distributions ◽  
Path Modelling ◽  
Low Latitude Ionosphere ◽  
Value Decomposition

Abstract. Equatorial ionosphere poses a challenge to any algorithm that is used for tomographic reconstruction because of the phenomena like the Equatorial Ionization Anomaly (EIA) and Equatorial Spread F (ESF). Any tomographic reconstruction of ionospheric density distributions in the equatorial region is not acceptable if it does not image these phenomena, which exhibit large spatial and temporal variability, to a reasonable accuracy. The accuracy of the reconstructed image generally depends on many factors, such as the satellite-receiver configuration, the ray path modelling, grid intersections and finally, the reconstruction algorithm. The present simulation study is performed to examine these in the context of the operational Coherent Radio Beacon Experiment (CRABEX) network just commenced in India. The feasibility of using this network for the studies of the equatorial and low-latitude ionosphere over Indian longitudes has been investigated through simulations. The electron density distributions that are characteristic of EIA and ESF are fed into various simulations and the reconstructed tomograms are investigated in terms of their reproducing capabilities. It is seen that, with the present receiver chain existing from 8.5° N to 34° N, it would be possible to obtain accurate images of EIA and the plasma bubbles. The Singular Value Decomposition (SVD) algorithm has been used for the inversion procedure in this study. As is known, by the very nature of ionospheric tomography experiments, the received data contain various kinds of errors, like the measurement and discretization errors. The sensitivity of the inversion algorithm, SVD in the present case, to these errors has also been investigated and quantified.

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