Simultaneous Algebraic Reconstruction Technique Method Research Articles

An Extended Simultaneous Algebraic Reconstruction Technique for Imaging the Ionosphere Using GNSS Data and Its Preliminary Results

To generate high-quality reconstructions of ionospheric electron density (IED), we propose an extended simultaneous algebraic reconstruction technique (ESART). The ESART method distributes the discrepancy between the actual GNSS TEC and the calculated TEC among the ray–voxels based on the contribution of voxels to GNSS TEC, rather than the ratio of the length of ray–voxel intersection to the sum of the lengths of all ray–voxel intersections, as is adopted by conventional methods. The feasibility of the ESART method for reconstructing the IED under different levels of geomagnetic activities is addressed. Additionally, a preliminary experiment is performed using the reconstructed IED profiles and comparing them with ionosonde measurements, which provide direct observations of electron density. The root mean square errors (RMSE) and absolute errors of the ESART method, the simultaneous algebraic reconstruction technique (SART) method, and the International Reference Ionosphere (IRI) 2016 model are calculated to evaluate the effectiveness of the proposed method. Compared to the conventional SART method of ionospheric tomography and the IRI-2016 model, the reconstructed IED profiles obtained using the ESART method are in better agreement with the electron density obtained from the ionosondes, especially for the peak electron densities (NmF2). In addition, a case study of an intense geomagnetic storm on 17–19 March 2015 shows that the spatial and temporal features of storm-related ionospheric disturbances can be more clearly depicted using the ESART method than with the SART method.

Radial Basis Function Coupled SART Method for Dynamic LAS Tomography

Laser absorption spectroscopy (LAS) tomography is an effective combustion diagnosis method for its simultaneous imaging of temperature and gas molar concentration. Only limited projections are available in many applications, the unknowns in the image reconstruction are much more, and it restricts the quality of reconstructed images. The radial basis function (RBF) is introduced to simplify the expressions of continuous distributions in the region of interest (ROI). The number of unknowns is greatly reduced, as gray values in the imaging region are depicted by the coefficient vector of these RBFs. The continuity in temperature distributions was coupled with the simultaneous algebraic reconstruction technique (SART) method. The coefficient vector of these RBFs and density distributions of integral absorbances were obtained. Gaussian compactly supported RBF was selected to reduce computation burden and reconstruction error. Performance comparisons between the proposed method and the classical SART method were made. The imaging quality of the proposed method was superior to SART, the temperature error was smaller than SART by nearly 10% and high spatial resolution was achieved. Dynamic flames in the McKenna burner and wind tunnel were used to verify its robustness and applicability in harsh cases.

Computationally Efficient System Matrix Calculation Techniques in Computed Tomography Iterative Reconstruction.

Background:Relative to classical methods in computed tomography, iterative reconstruction techniques enable significantly improved image qualities and/or lowered patient doses. However, the computational speed is a major concern for these iterative techniques. In the present study, we present a method for fast system matrix calculation based on the line integral model (LIM) to speed up the computations without compromising the image quality. In addition, we develop a hybrid line–area integral model (AIM) that highlights the advantages of both LIM and AIMs.Methods:The contributing detectors for a given pixel and a given projection view, and the length of corresponding intersection lines with pixels, are calculated using our proposed algorithm. For the hybrid method, the respective narrow-angle fan beam was modeled by multiple equally spaced lines. The computed system matrix was evaluated in the context of reconstruction using the simultaneous algebraic reconstruction technique (SART) as well as maximum likelihood expectation maximization (MLEM).Results:The proposed LIM offers a considerable reduction in calculation times compared to the standard Siddon algorithm: 2.9 times faster. Differences in root mean square error and peak signal-to-noise ratio were not significant between the proposed LIM and the Siddon algorithm for both SART and MLEM reconstruction methods (P > 0.05). Meanwhile, the proposed hybrid method resulted in significantly improved image qualities relative to LIM and the Siddon algorithm (P < 0.05), though computations were 4.9 times more intensive than the proposed LIM.Conclusion:We have proposed two fast algorithms to calculate the system matrix. The first is based on LIM and was faster than the Siddon algorithm, with matched image quality, whereas the second method is a hybrid LIM–AIM that achieves significantly improved images though with its computational requirements.

Development of a chest digital tomosynthesis R/F system and implementation of low-dose GPU-accelerated compressed sensing (CS) image reconstruction.

This work describes the hardware and software developments of a prototype chest digital tomosynthesis (CDT) R/F system. The purpose of this study was to validate the developed system for its possible clinical application on low-dose chest tomosynthesis imaging. The prototype CDT R/F system was operated by carefully controlling the electromechanical subsystems through a synchronized interface. Once a command signal was delivered by the user, a tomosynthesis sweep started to acquire 81 projection views (PVs) in a limited angular range of ±20°. Among the full projection dataset of 81 images, several sets of 21 (quarter view) and 41 (half view) images with equally spaced angle steps were selected to represent a sparse view condition. GPU-accelerated and total-variation (TV) regularization strategy-based compressed sensing (CS) image reconstruction was implemented. The imaged objects were a flat-field using a copper filter to measure the noise power spectrum (NPS), a Catphan® CTP682 quality assurance (QA) phantom to measure a task-based modulation transfer function (MTFTask ) of three different cylinders' edge, and an anthropomorphic chest phantom with inserted lung nodules. The authors also verified the accelerated computing power over CPU programming by checking the elapsed time required for the CS method. The resultant absorbed and effective doses that were delivered to the chest phantom from two-view digital radiographic projections, helical computed tomography (CT), and the prototype CDT system were compared. The prototype CDT system was successfully operated, showing little geometric error with fast rise and fall times of R/F x-ray pulse less than 2 and 10 ms, respectively. The in-plane NPS presented essential symmetric patterns as predicted by the central slice theorem. The NPS images from 21 PVs were provided quite different pattern against 41 and 81 PVs due to aliased noise. The voxel variance values which summed all NPS intensities were inversely proportional to the number of PVs, and the CS method gave much lower voxel variance by the factors of 3.97-6.43 and 2.28-3.36 compared to filtered backprojection (FBP) and 20 iterations of simultaneous algebraic reconstruction technique (SART). The spatial frequencies of the f50 at which the MTFTask reduced to 50% were 1.50, 1.55, and 1.67 cycles/mm for FBP, SART, and CS methods, respectively, in the case of Bone 20% cylinder using 41 views. A variety of ranges of TV reconstruction parameters were implemented during the CS method and we could observe that the NPS and MTFTask preserved best when the regularization and TV smoothing parameters α and τ were in a range of 0.001-0.1. For the chest phantom data, the signal difference to noise ratios (SDNRs) were higher in the proposed CS scheme images than in the FBP and SART, showing the enhanced rate of 1.05-1.43 for half view imaging. The total averaged reconstruction time during 20 iterations of the CS scheme was 124.68 s, which could match-up a clinically feasible time (<3 min). This computing time represented an enhanced speed 386 times greater than CPU programming. The total amounts of estimated effective doses were 0.12, 0.53 (half view), and 2.56 mSv for two-view radiographs, the prototype CDT system, and helical CT, respectively, showing 4.49 times higher than conventional radiography and 4.83 times lower than a CT exam, respectively. The current work describes the development and performance assessment of both hardware and software for tomosynthesis applications. The authors observed reasonable outcomes by showing a potential for low-dose application in CDT imaging using GPU acceleration.

Evaluation of electron tomography reconstruction methods for interface roughness measurement.

We evaluate the suitability of simultaneous iterative reconstruction technique (SIRT), filtered back projection, and simultaneous algebraic reconstruction technique methods for buried interface roughness measurements. We also investigate the effect of total electron dose distributed over the entire tilt series on measured roughness values. We investigate the applicability of the dose fractionation theorem by evaluating the effect of an increasing number of images, i.e., decreasing tilt increment size at fixed total electron irradiation dose on the quantitative measurement of buried interface roughness. The results indicate that SIRT is the most suitable method for reconstruction and a 3° to 5° angle is optimal for the roughness measurement.

Fast Projection Algorithm for LIM-Based Simultaneous Algebraic Reconstruction Technique and Its Parallel Implementation on GPU

Simultaneous algebraic reconstruction technique (SART) is a well-known iterative method in X-ray computed tomography, which provides better image quality than analytical methods when dealing with incomplete or noisy data. The disadvantage of SART is the slow speed compared with the analytical methods. Since forward projection and backprojection are two major time-consuming operations in iterative reconstruction, we propose an algorithm for fast forward projection and improved backprojection for the line integral model-based SART. Using the proposed algorithm, the SART method was implemented on a GPU platform with NVIDIA’s parallel computing architecture. Both computer simulations and physical phantom experiments were carried out, and their results show that our approach is highly efficient and accurate. The computation time for the system matrix using our proposed projector is 10 times faster than that using the Siddon’s projector, and our improved backprojection algorithm is 1.5 times faster than Li’s method in determining the minimum bounding interval. The GPU-based SART using our proposed projection algorithm can obtain about 7.4 times reconstruction speed-up compared with that using the traditional projection approach, while preserving the accuracy of the results.

Simultaneous deblurring and iterative reconstruction of CBCT for image guided brain radiosurgery

One of the limiting factors in cone-beam CT (CBCT) image quality is system blur, caused by detector response, x-ray source focal spot size, azimuthal blurring, and reconstruction algorithm. In this work, we develop a novel iterative reconstruction algorithm that improves spatial resolution by explicitly accounting for image unsharpness caused by different factors in the reconstruction formulation. While the model-based iterative reconstruction techniques use prior information about the detector response and x-ray source, our proposed technique uses a simple measurable blurring model. In our reconstruction algorithm, denoted as simultaneous deblurring and iterative reconstruction (SDIR), the blur kernel can be estimated using the modulation transfer function (MTF) slice of the CatPhan phantom or any other MTF phantom, such as wire phantoms. The proposed image reconstruction formulation includes two regularization terms: (1) total variation (TV) and (2) nonlocal regularization, solved with a split Bregman augmented Lagrangian iterative method. The SDIR formulation preserves edges, eases the parameter adjustments to achieve both high spatial resolution and low noise variances, and reduces the staircase effect caused by regular TV-penalized iterative algorithms. The proposed algorithm is optimized for a point-of-care head CBCT unit for image-guided radiosurgery and is tested with CatPhan phantom, an anthropomorphic head phantom, and 6 clinical brain stereotactic radiosurgery cases. Our experiments indicate that SDIR outperforms the conventional filtered back projection and TV penalized simultaneous algebraic reconstruction technique methods (represented by adaptive steepest-descent POCS algorithm, ASD-POCS) in terms of MTF and line pair resolution, and retains the favorable properties of the standard TV-based iterative reconstruction algorithms in improving the contrast and reducing the reconstruction artifacts. It improves the visibility of the high contrast details in bony areas and the brain soft-tissue. For example, the results show the ventricles and some brain folds become visible in SDIR reconstructed images and the contrast of the visible lesions is effectively improved. The line-pair resolution was improved from 12 line-pair/cm in FBP to 14 line-pair/cm in SDIR. Adjusting the parameters of the ASD-POCS to achieve 14 line-pair/cm caused the noise variance to be higher than the SDIR. Using these parameters for ASD-POCS, the MTF of FBP and ASD-POCS were very close and equal to 0.7 mm−1 which was increased to 1.2 mm−1 by SDIR, at half maximum.

Study of low-latitude ionosphere over Indian region using simultaneous algebraic reconstruction technique

Recognizing the advantages of simultaneous algebraic reconstruction technique (SART), it is applied to investigate the electron density distribution of low-latitude ionosphere. The total electron content data measured at three receivers in West Bengal, India, are used in this analysis. The efficiency of SART in the reconstruction of large scale ionospheric structure is addressed through reconstruction of ionization anomaly. Comparison with the model ionospheric data ensures the accuracy of the SART method for the reconstruction at low-latitude region. Also, a case study with different reconstruction geometry reveals the ability of fast convergence of simultaneous algebraic reconstruction algorithm irrespective of the geometry.

Data fusion in X-ray computed tomography using a superiorization approach.

X-ray computed tomography (CT) is an important and widespread inspection technique in industrial non-destructive testing. However, large-sized and heavily absorbing objects cause artifacts due to either the lack of penetration of the specimen in specific directions or by having data from only a limited angular range of views. In such cases, valuable information about the specimen is not revealed by the CT measurements alone. Further imaging modalities, such as optical scanning and ultrasonic testing, are able to provide data (such as an edge map) that are complementary to the CT acquisition. In this paper, a superiorization approach (a newly developed method for constrained optimization) is used to incorporate the complementary data into the CT reconstruction; this allows precise localization of edges that are not resolvable from the CT data by itself. Superiorization, as presented in this paper, exploits the fact that the simultaneous algebraic reconstruction technique (SART), often used for CT reconstruction, is resilient to perturbations; i.e., it can be modified to produce an output that is as consistent with the CT measurements as the output of unmodified SART, but is more consistent with the complementary data. The application of this superiorized SART method to measured data of a turbine blade demonstrates a clear improvement in the quality of the reconstructed image.

Weld Defect Detection Using Iterative Image Reconstruction Methods

Non Destructive Evaluation (NDE) is a technique to detect the defects without affecting the intended application or the structure, which is mainly used for damage assessment and quality control. NDE is basically used for automation of defect quantification. This paper presents a method for weld defect detection using iterative method for image reconstruction. Image reconstruction is a technique of reconstructing the image of object from the radon transform of the object, where radon transform is obtained by passing an energy source through the object in various angles and collecting the projected data on a detector. Weld defects such as slag inclusion, lack of penetration, and burn through can cause serious disaster if it is undetected at the time of weld process. The system of linear equation under consideration in Computed Tomography (CT) are basically very large in size, so the direct method takes too much of computational time which makes it impractical for implementation. Cimmino's method and Simultaneous Algebraic Reconstruction Technique (SART) are iterative methodologies for image reconstruction which are best suited for solving large scale linear system where direct method fails due to very large time consumption. This paper compares the experimental results of image reconstruction of weld defect radiographic images using SART and Cimmino's method for various test images with varying number of projections.

Convergence analysis of SART: optimization and statistics

Simultaneous algebraic reconstruction technique (SART) [A. Andersen, Algebraic reconstruction in CT from limited views, IEEE Trans. Med. Imaging 8 (1989), pp. 50–55; A. Andersen and A. Kak, Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm, Ultrason. Imaging 6 (1984), pp. 81–94] is an iterative method for solving inverse problems of form Ax(+n)=b. These kinds of problems arise, for example, in computed tomography (CT) reconstruction, in which case A is obtained from the discrete Radon transform. In this paper, we provide several methods for derivation of SART and connections between SART and other methods. Using these connections, we also prove the convergence of SART in different ways. These approaches are from optimization and statistical points of view and can be applied to other Landweber-like schemes such as Cimmino's algorithm and component averaging. Furthermore, the noisy case is considered and the error estimation is given. Several numerical experiments for CT reconstruction are provided to demonstrate the convergence results in practice.

Constrained SART algorithm for inverse problems in image reconstruction

In this paper we integrate the SART (Simultaneous Algebraic Reconstruction Technique) algorithm into a general iterative method, introduced in [8]. This general method offers us the possibility of achieving a new convergence proof of the SART method and prove the convergence of the constrained version of SART. Systematic numerical experiments, comparing SART and Kaczmarz-like algorithms, are made on two phantoms widely used in image reconstruction literature.

A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis.

Digital tomosynthesis mammography (DTM) is a promising new modality for breast cancer detection. In DTM, projection-view images are acquired at a limited number of angles over a limited angular range and the imaged volume is reconstructed from the two-dimensional projections, thus providing three-dimensional structural information of the breast tissue. In this work, we investigated three representative reconstruction methods for this limited-angle cone-beam tomographic problem, including the backprojection (BP) method, the simultaneous algebraic reconstruction technique (SART) and the maximum likelihood method with the convex algorithm (ML-convex). The SART and ML-convex methods were both initialized with BP results to achieve efficient reconstruction. A second generation GE prototype tomosynthesis mammography system with a stationary digital detector was used for image acquisition. Projection-view images were acquired from 21 angles in 3 degrees increments over a +/- 30 degrees angular range. We used an American College of Radiology phantom and designed three additional phantoms to evaluate the image quality and reconstruction artifacts. In addition to visual comparison of the reconstructed images of different phantom sets, we employed the contrast-to-noise ratio (CNR), a line profile of features, an artifact spread function (ASF), a relative noise power spectrum (NPS), and a line object spread function (LOSF) to quantitatively evaluate the reconstruction results. It was found that for the phantoms with homogeneous background, the BP method resulted in less noisy tomosynthesized images and higher CNR values for masses than the SART and ML-convex methods. However, the two iterative methods provided greater contrast enhancement for both masses and calcification, sharper LOSF, and reduced interplane blurring and artifacts with better ASF behaviors for masses. For a contrast-detail phantom with heterogeneous tissue-mimicking background, the BP method had strong blurring artifacts along the x-ray source motion direction that obscured the contrast-detail objects, while the other two methods can remove the superimposed breast structures and significantly improve object conspicuity. With a properly selected relaxation parameter, the SART method with one iteration can provide tomosynthesized images comparable to those obtained from the ML-convex method with seven iterations, when BP results were used as initialization for both methods.

USART 방법에 의한 X선 영상으로부터의 삼차원 물체의 형상 복원

Inspection and shape measurement of three-dimensional objects are widely needed in industries for quality monitoring and control. A number of visual or optical technologies have been successfully applied to measure three-dimensional surfaces. However, those conventional visual or optical methods have inherent shortcomings such as occlusion and variant surface reflection. X-ray vision system can be a good solution to these conventional problems, since we can extract the volume information including both the surface geometry and the inner structure of any objects. In the x-ray system, the surface condition of an object, whether it is lambertian or specular, does not affect the inherent characteristics of its x-ray images. In this paper, we propose a three-dimensional x-ray imaging method to reconstruct a three dimensional structure of an object out of two dimensional x-ray image sets. To achieve this by the proposed method, two or more x-ray images projected from different views are needed. Once these images are acquired, the simultaneous algebraic reconstruction technique(SART) is usually utilized. Since the existing SART algorithms have several shortcomings such as low performance in convergence and different convergence within the reconstruction volume of interest, an advanced SART algorithm named as USART(uniform SART) is proposed to avoid such shortcomings and improve the reconstruction performance. Because, each voxel within the volume is equally weighted to update instantaneous value of its internal density, it can achieve uniform convergence property of the reconstructed volume. The algorithm is simulated on various shapes of objects such as a pyramid, a hemisphere and a BGA model. Based on simulation results the performance of the proposed method is compared with that of the conventional SART method.

Holographic tomography by SART and it's application to reconstruction of 3D temperature distribution

Application of holographic tomography to reconstruction of 3D asymmetric temperature distribution is experimentally and numerically investigated. A new simultaneous algebraic reconstruction technique (SART) code for holographic tomography is presented. Important features of SART for reconstruction of temperature field were evaluated using numerical model functions. Data from diffuse-illumination holographic interferograms obtained at twenty different view directions and with 40° range of view angles were used to reconstruct a 3D thermal flow field by SART method. An average reconstruction error of about 5% is estimated. The ability to reconstruct the 3D field using a limited viewing range implies that SART is especially suitable for the holographic tomography of aerodynamic density field.