An Algebraic Iterative Algorithm for Determining the Equilibrium State of the Completed Suspension Bridge Based on Explicit Calculation of Reasonable Hanger Forces

In this paper, a unified framework of iterative algebraic reconstruction for emission computed tomography (ECT) and its application to positron emission tomography (PET) is presented. The unified framework is based on an algebraic image restoration model and contains conventional iterative algebraic reconstruction algorithms: ART, SIRT, Landweber iteration (LWB), the generalized Landweber iteration (GLWB), the steepest descent method (STP), as well as iterative filtered backprojection (IFBP) reconstruction algorithms: Chang's method, Walters' method, and a modified iterative MAP. The framework provides an effective tool to systematically study conventional iterative algebraic algorithms and IFBP algorithms. Based on this framework, conventional iterative algebraic algorithms and IFBP algorithms are generalized. It is shown from the algebraic point of view that IFBP algorithms are not only excellent methods for correction of attenuation (either uniform or nonuniform) but are also good general iterative reconstruction algorithms (they can be applied to either attenuated or attenuation-free projections and converge very fast). The convergence behavior of iterative algebraic algorithms is discussed and insight is drawn into the fast convergence property of IFBP algorithms. A simulated PET system is used to evaluate IFBP algorithms and LWB in comparison with the maximum likelihood estimation via expectation maximization algorithm (MLE-EM) and the filtered backprojection (FBP) algorithm. The simulation results indicate that for both attenuation-free projection and attenuated projection cases IFBP algorithms have a significant computational advantage over LWB and MLE-EM, and have performance advantages over FBP in terms of contrast recovery and/or noise-to-signal ratios (NSRs) in regions of interest.

Three different PET image reconstruction techniques were evaluated to quantita­tively measure the 18F-labeled cytostatic agent 5-fluorouracil (5-[18F]FU) in liver metastases of tumor patients: the standard filtered back-projector and two iterative algebraic algorithms with successive overrelaxation for accelerated convergence. Forward-projected activity distributions with different counting statistics were simulated using random number generators based on Poisson processes. The algebraic algorithms were numerically stable with the calculated concen­trations uniformly converging to the theoretical values. The lesion contrast improved with the number of iterations, but was accompanied by increasing image noise. More than 80 iteration steps were necessary to accurately quantify the drug 5-[18F]FU in the metastases (error ≤ 20%).

An improved algebraic iterative algorithm was proposed to solve the problem that reconstruction of gas diffusion can barely be completed by the conventional algebraic iterative algorithm.Under the condition of fan beam geometry and double projections,the prior matrix was introduced in the iteration steps and the results processed by median filter every few iterations.Taking Gaussian plume model as test object,the effect of iterations,relaxation factor and different filter using strategies on the reconstruction results were analyzed.The experimental results shows that the mean square error and peak error reach the basic convergence and the peaks can be controlled in a certain range when the number of iterations is 500 and the relaxation factor is 2.Compared with the conventional algebraic iterative algorithm,the improved algorithm is better on the reconstitution indicators of mean square error and peak error.Furthermore,the peak position can be located more accurately and tail peak can be reconstructed successfully through the improved algorithm and the improved algorithm is robust to noise.

A novel algebraic iterative algorithm based on deflection tomography is presented. This algorithm is derived from the essentials of deflection tomography with a linear expansion of the local basis functions. By use of this algorithm the tomographic problem is finally reduced to the solution of a set of linear equations. The algorithm is demonstrated by mapping a three-peak Gaussian simulative temperature field. Compared with reconstruction results obtained by other traditional deflection algorithms, its reconstruction results provide a significant improvement in reconstruction accuracy, especially in cases with noisy data added. In the density diagnosis of a hypersonic wind tunnel, this algorithm is adopted to reconstruct density distributions of an axial symmetry flow field. One cross section of the reconstruction results is selected to be compared with the inverse Abel transform algorithm. Results show that the novel algorithm can achieve an accuracy equivalent to the inverse Abel transform algorithm. However, the novel algorithm is more versatile because it is applicable to arbitrary kinds of distribution.

X-ray phase contrast imaging (PCI) has great potential in the medical diagnosis, material science et al and has made great progress in the last ten years. Diffraction enhanced imaging and grating-based imaging are the two significant methods for PCI, currently. Two methods are named differential phase contrast imaging because the projection data is partial derivatives of refractive index. Analytical algorithms to reconstruct the refractive index have been proposed. However, there is lack of an iterative algorithm to reconstruct the refractive index directly from the refraction angle data. In this paper, an algebraic iterative algorithm is proposed to reconstruct the distribution of refractive index from refraction angle data. Our algorithm is a complementarity to analytical reconstruction algorithms and inherits the benefits of iterative algorithms that can work well with in-complete projection data. The proposed algorithm is validated by numerical simulation and the results show that it can reconstruct refractive index accurately and the iteration is convergent and steady.

The objective of this study was to compare the diagnostic value of computed tomography (CT) based on iterative reconstruction algorithm in old myocardial infarction (OMI), thereby providing theoretical guidance and practical basis for clinical treatment. In this study, in order to provide theoretical guidance and practical basis for the diagnosis and treatment of clinical OMI, 10 patients with OMI were selected and divided into two groups, with 5 patients in each group. In addition, an algebraic iterative reconstruction algorithm is constructed, which starts from the initial estimation value, compares, and corrects the estimation results and the measured results continuously until the error between the two results is less than the predetermined value. The experimental group was optimized by algebraic iterative reconstruction algorithm, and the control group was reconstructed by the hospital original method. The image quality parameters under different iteration times were analyzed and compared to obtain the optimal iteration times. The value of iterative reconstruction algorithm in clinical diagnosis was investigated by analyzing the time of drawing and the accuracy of diagnosis after drawing. Through the analysis and comparison of the image quality parameters of the patients from the experimental group, it was found that the image quality firstly increased with the increase in the number of iterations but decreased with the increase of the number of iterations after a certain number of iterations. The results showed that the optimal number of iterations was 13 times. The drawing time of the experimental group and the control group was 54.27 minutes and 117.87 minutes in turn, so the difference between the two groups was significant (P < 0.05). Besides, there was a statistically marked difference in the accuracy rate of the experimental group (93.33%) and the control group (73.33%) (P < 0.05). In conclusion, the time required for coronary artery CT imaging using algebraic iterative reconstruction algorithm was greatly reduced and the diagnostic accuracy was hugely improved. Therefore, the coronary artery CT imaging based on iterative reconstruction algorithm could make more effective use of medical resources and improve the diagnostic accuracy in the diagnosis of OMI.

Determining the hanger force of the suspension bridge with short extended spans: An analytical algorithm

Iterative CT reconstruction algorithms coupled with edge-preserving filters are attracting a growing interest in the field of biomedical X-ray imaging. In many cases the application of such algorithms results in an improved reconstruction quality when compared with filtered back-projection (FBP). Iterative algorithms commonly entail a decrease of image noise or, equivalently, an increase of contrast-to-noise ratio, while preserving image detail. Conversely, they modify the shape of noise power spectrum, producing a shift towards lower spatial frequencies with respect to FBP. This results in a patchy or waxy appearance of the reconstructed images. Changes in image texture affect radiologists’ perception of image quality, possibly influencing their willingness to use an iterative algorithm in clinical practice. In this work we present a GPU implementation of a simultaneous algebraic reconstruction technique algorithm, combined with a bilateral regularization filter, and we discuss the optimization of the algorithm’s parameters in terms of noise texture, selecting those parameters which preserve its natural appearance. We evaluated the performances of the algorithm, compared to FBP, both on a test phantom and on a surgical mastectomy sample by using contrast-to-noise ratio and spatial resolution metrics. Samples were imaged at the SYRMEP beamline of the Elettra synchrotron facility with a monochromatic beam (32 keV) in propagation-based phase-contrast configuration, delivering a clinically-compatible radiation dose of 5 mGy and using a large-area CdTe photon-counting detector. Results show, in the specific application on breast specimens, that the implemented algorithm can be tuned to preserve the noise texture and spatial resolution observed in FBP reconstructions, while improving contrast-to-noise ratio up to 30%.

A fast-iterative reconstruction algorithm for sparse angle CT based on compressed sensing

A diffraction-based technique is developed for the determination of three-dimensional nanostructures. The technique employs high-resolution and low-dose scanning electron nanodiffraction (SEND) to acquire three-dimensional diffraction patterns, with the help of a special sample holder for large-angle rotation. Grains are identified in three-dimensional space based on crystal orientation and on reconstructed dark-field images from the recorded diffraction patterns. Application to a nanocrystalline TiN thin film shows that the three-dimensional morphology of columnar TiN grains of tens of nanometres in diameter can be reconstructed using an algebraic iterative algorithm under specified prior conditions, together with their crystallographic orientations. The principles can be extended to multiphase nanocrystalline materials as well. Thus, the tomographic SEND technique provides an effective and adaptive way of determining three-dimensional nanostructures.

One of the main problems related to the design of suspension bridges is stabilisation of their initial form. The tendency of suspension bridges to deform is generally determined by the kinematical displacements of the suspension cable caused by asymmetrical loads rather than by the elastic deformations. There are some suspension bridges when the so‐called rigid (stiff in bending) cables instead of usual flexible cables are suggested for stabilisation of their initial form. The analysis methods of such suspension bridges with rigid cables are underdeveloped. For the analysis of classical suspension bridges analytical models can be applied. However, in case of concentrated forces, the numerical techniques are preferred. The article presents analytical expressions for the calculation of internal forces and displacements of suspension bridges with a rigid cable. The article also discusses the discrete calculation model for classical suspension bridges. Santrauka Viena iš pagrindiniu kabamuju tiltu projektavimo problemu yra pradinus ju formos stabilizavimas. Kabamuju tiltu deformatyvuma lemia iš esmes ne tiek tampriosios deformacijos, kiek asimetriniu apkrovu sukelti kinematiniai kabamojo lyno poslinkiai. Yra žinomi kabamieji tiltai, kuriu pradinei formai stabilizuoti siūloma vietoje iprastiniu lanksčiuju lynu taikyti vadinamuosius standžius lynus. Tokiu kabamuju tiltu su standžiaislynais skaičiavimo metodai nera iki galo parengti. Klasikiniams tiltams su lanksčiu lynu skaičiuoti taikomi daugiausia kontinualūs modeliai, kurie esant tam tikrai tilto sandarai ar veikiant sutelktoms apkrovoms nera pakankamai tikslūs. Straipsnyje pateikiamos analizines išraiškos kabamuju tiltu su standžiu lynu iražoms ir poslinkiams apskaičiuoti, aptariamas diskretusis klasikiniu kabamuju tiltu skaičiavimo modelis.

An algorithm for fast calculation of short circuit forces in high current busbars of electric arc furnace transformers based on method of images

To accelerate iterative algebraic reconstruction algorithms using a cylindrical image grid. Tetrahedron beam computed tomography (TBCT) is designed to overcome the scatter and detector problems of cone beam computed tomography (CBCT). Iterative algebraic reconstruction algorithms have been shown to mitigate approximate reconstruction artifacts that appear at large cone angles, but clinical implementation is limited by their high computational cost. In this study, a cylindrical voxelization method on a cylindrical grid is developed in order to take advantage of the symmetries of the cylindrical geometry. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as CBCT and TBCT. This method was implemented in combination with the simultaneous algebraic reconstruction technique (SART). Both two- and three-dimensional numerical phantoms as well as a patient CT image were utilized to generate the projection sets used for reconstruction. The reconstructed images were compared to the original phantoms using a set of three figures of merit (FOM). The cylindrical voxelization on a cylindrical reconstruction grid was successfully implemented in combination with the SART reconstruction algorithm. The FOM results showed that the cylindrical reconstructions were able to maintain the accuracy of the Cartesian reconstructions. In three dimensions, the cylindrical method provided better accuracy than the Cartesian methods. At the same time, the cylindrical method was able to provide a speedup factor of approximately 40 while also reducing the system matrix storage size by 2 orders of magnitude. TBCT image reconstruction using a cylindrical image grid was able to provide a significant improvement in the reconstruction time and a more compact system matrix for storage on the hard drive and in memory while maintaining the image quality provided by the Cartesian voxelization on a Cartesian grid.

In this paper, a hardware in the loop (HIL) scheme using a polynomial approximation for the calculation of aerodynamic forces associated with wind turbine blades is presented. The proposed approach allows the real-time calculation of forces acting on a blade for use as input data for a force emulating system. The blade element momentum (BEM) theory was used to calculate the axial and tangential forces, but an iterative algorithm needs to be executed for each time of the system’s operation. In order to allow a real-time calculation, the BEM algorithm can be executed for a range of rotor angular speeds, wind velocities, and pitch angles covering the conditions under which the wind turbine will operate. The resulting power, torque, and forces are then approximated by polynomials and implemented in an HIL test facility. A comparison between the results obtained from the BEM algorithm and polynomials demonstrates the accuracy of the proposed approach. An experimental setup comprised of the software used for the force and pitch angle calculation and the hardware used for the force emulation and pitch angle control is presented. Experimental results obtained with the system running in real-time demonstrate the ability to apply effective moments without the need for an extensive test structure.

An approach for calculation of reaction and friction forces between pairs of bodies in spatial mechanical systems, as well as contact points in joints with clearances is presented. Coulomb friction is taken into consideration. Problems are solved iteratively, to satisfy both kinematic and dynamic equations. Matrix methods are used to derive the nonlinear kinematic constraint equations. Newton-Euler dynamic equations are applied for solution of direct and inverse problems of dynamics. External and inertia forces for each configuration of the kinematic chain the contact points and corresponding normal forces are calculated. Relative positions of the coordinate systems of the links are computed and, their new positions relative to the inertia reference frame are estimated. An iterative algorithm is suggested for calculation of forces and computing generalized coordinate increments for achieving the prescribed accuracy of system end-effectors. Kinematic and dynamic equivalents of rotational, translational, and prismatic pairs with clearances are suggested. A model of joints with clearances is applied for solution of the direct and inverse problems of dynamics, taking into account presence of unilateral reactions, viscous friction, contact friction, and impact in bearings. An example of a triple pendulum with rotational pairs, a driving force on the end-effector, and large clearances is presented.