Two-step Reconstruction Method Research Articles

Meso-scale simulation of Li–O2 battery discharge process by an improved lattice Boltzmann method

The discharge process of lithium–oxygen battery (LOB) is a highly complicated multi-physics coupling phenomenon. Moreover, the cathode morphology presents a complex multi-scale structure with pore size ranging from nanometers to micronmeters, and plays a crucial role in determining the discharge performance. In this work, the cathodes consisting of carbon paper, electrode material, and electrolyte are first numerically reconstructed using a two-step reconstruction method considering the multi-scale morphology. A lattice Boltzmann model with an improved partial bounce-back scheme is proposed for modeling the discharge process given that the electrode porosity changes with the progress of discharge. The effects of micron-scale electrode spatial distribution on the O2 diffusion and LOB discharge performance are investigated. Results show that the increment of the electrode dispersion degree increases the O2 diffusion resistance due to the increase of electrolyte-electrode specific interface area. A large local electrode load near O2 inlet leads to a high O2 diffusion resistance and low O2 concentration owing to the large specific interface area and electrode volume. Cathodes with the minimum electrode load and maximum electrode dispersion degree present the optimal specific capacity of LOB. However, the specific capacity first increases significantly and then slightly decreases with the increase of local electrode load.

A Novel Reconstruction Method for Temperature Distribution Measurement Based on Ultrasonic Tomography.

The precise temperature distribution measurement is crucial in many industrial fields, where ultrasonic tomography (UT) has broad application prospects and significance. In order to improve the resolution of reconstructed temperature distribution images and maintain high accuracy, a novel two-step reconstruction method is proposed in this article. First, the problem of solving the temperature distribution is converted to an optimization problem and then solved by an improved version of the equilibrium optimizer (IEO), in which a new nonlinear time strategy and novel population update rules are deployed. Then, based on the low-resolution and high-precision images reconstructed by IEO, Gaussian process regression (GPR) is adopted to enhance image resolution and keep the reconstruction errors low. After that, the number of divided grids and the parameters of IEO are also further studied to improve the reconstruction quality. The results of numerical simulations and experiments indicate that high-resolution images with low reconstruction errors can be reconstructed effectively by the proposed IEO-GPR method, and it also shows excellent robust performance. For a complex three-peak temperature distribution, a competitive accuracy with 3.10% and 2.37% error at root-mean-square error and average relative error is achieved, respectively. In practical experiment, the root-mean-square error of IEO-GPR is 0.72%, which is at least 0.89% lower than that of conventional algorithms.

A Two-Step Surface Reconstruction Method Using Signed Marching Cubes

In this paper, we explore a new approach, a two-step surface reconstruction method to extract the target isosurface from a given implicit function efficiently. Our main contribution is that we improve the surface reconstruction process by accelerating the speed of evaluation using signed marching cubes. The basic strategy is to filter the invalid voxels that do not intersect with the target isosurface in a low-cost manner, and to evaluate the valid voxels that intersect with the target isosurface accurately. The improved signed marching cubes method consists of a rough evaluation step and an exact evaluation step. The coarse evaluation step evaluates the points of all voxels using the fast multipole method with a lower order. After the rough evaluation step, the voxels that intersect with the target isosurface are screened out. Then, the exact evaluation step evaluates the points of filtered voxels using the fast multipole method with a higher order. The experimental results show that, compared with the traditional marching cubes method, the improved reconstruction method reduces the amounts of calculation for invalid voxels that do not intersect with the target isosurfaces, which is useful to improve the efficiency of surface reconstruction.

Parametric Reconstruction Method for the Long Time-Series Return-Stroke Current of Triggered Lightning Based on the Particle Swarm Optimization Algorithm

The lightning research group of the Chinese Academy of Meteorological Sciences has carried out observations and experiments with artificially triggered lightning for more than ten years, and it accumulated thousands of examples of channel base current data on the return stroke of artificially triggered lightning prior to 2020. Based on the current data, this paper explores ways of improving the constructed function of a long time-series (400 μs) return stroke and the parametric reconstruction of the current waveform. The long time-series current can be divided into three components: the breakdown pulse current, corona current and quasi-uniform current. The corona current and quasi-uniform current are constructed by a Heidler function, while the breakdown pulse current is determined by the waveform characteristics of the current peak, which can be divided into the Heidler type and high-order exponential type. According to the three-component model of the return-stroke current, a two-step parametric reconstruction method for the long time-series lightning return-stroke current based on the particle swarm optimization (PSO) algorithm is proposed. In this paper, the results of the parameterized reconstruction of 14 return strokes are given, and the results of the multidimensional error analysis of 13 long time-series return strokes are given to illustrate the accuracy of the improved parameterized model of the return-stroke current and the effectiveness of the two-step reconstruction method based on the PSO algorithm.

Full Field Inversion in Photoacoustic Tomography with Variable Sound Speed

To accelerate photoacoustic data acquisition, in [R. Nuster, G. Zangerl, M. Haltmeier, G. Paltauf (2010). Full field detection in photoacoustic tomography. Optics express, 18(6), 6288–6299] a novel measurement and reconstruction approach has been proposed, where the measured data consist of projections of the full 3D acoustic pressure distribution at a certain time instant T. Existing reconstruction algorithms for this kind of setup assume a constant speed of sound. This assumption is not always met in practice and thus can lead to erroneous reconstructions. In this paper, we present a two-step reconstruction method for full field detection photoacoustic tomography that takes variable speed of sound into account. In the first step, by applying the inverse Radon transform, the pressure distribution at the measurement time is reconstructed point-wise from the projection data. In the second step, a final time wave inversion problem is solved where the initial pressure distribution is recovered from the known pressure distribution at time T. We derive an iterative solution approach for the final time wave inversion problem and compute the required adjoint operator. Moreover, as the main result of this paper, we derive its uniqueness and stability. Our numerical results demonstrate that the proposed reconstruction scheme is fast and stable, and that ignoring sound speed variations significantly degrades the reconstruction.

A 3D Lagrangian cell-centered hydrodynamic method with higher-order reconstructions for gas and solid dynamics

The Lagrangian finite volume cell-centered hydrodynamic method introduces dissipation into the calculation by solving a multidirectional approximate Riemann problem. The amount of dissipation created is a function of the jump in the velocity and stress at the node. These jumps in velocity and stress can be reduced by using higher-order reconstructions that are constructed by fitting cell-average values in neighboring cells. One challenge is that a large stencil is required to create high-order reconstructions. To address this challenge, a new two-step reconstruction process is proposed to build a quadratic polynomial by only communicating with face-neighboring cells. The two-step reconstruction method is applied to scalar, vector, and tensor fields. Another challenge is that limiters must be used to reduce the higher order reconstructions towards piecewise constant fields near discontinuities to prevent artificial new extrema. We address this second challenge and propose a new hierarchical limiter that uses a discrete Mach number as a smoothness indicator. The inclusion of the Mach number is essential for minimizing dissipation errors. The new limiter is used with the reconstructions of pressure, velocity, and deviatoric stress. The accuracy and robustness of the new two-step reconstruction method with the new limiter is demonstrated by simulating a suite of 3D Cartesian test problems covering both gas and solid dynamics.

Two step imaging reconstruction using truncated pseudoinverse as a preliminary estimate in ultrasound guided diffuse optical tomography

Due to the correlated nature of diffused light, the problem of reconstructing optical properties using diffuse optical tomography (DOT) is ill-posed. US-, MRI- or x-ray-guided DOT approaches can reduce the total number of parameters to be estimated and improve optical reconstruction accuracy. However, when the target volume is large, the number of parameters to estimate can exceed the number of measurements, resulting in an underdetermined imaging model. In such cases, accurate image reconstruction is difficult and regularization methods should be employed to obtain a useful solution. In this manuscript, a simple two-step reconstruction method that can produce useful image estimates in DOT is proposed and investigated. In the first step, a truncated Moore-Penrose Pseudoinverse solution is computed to obtain a preliminary estimate of the image that can be reliably determined from the measured data; subsequently, this preliminary estimate is incorporated into the design of a penalized least squares estimator that is employed to compute the final image estimate. By use of phantom data, the proposed method was demonstrated to yield more accurate images than those produced by conventional reconstruction methods. The method was also evaluated with clinical data that included 10 benign and 10 malignant cases. The capability of reconstructing high contrast malignant lesions was demonstrated to be improved by use of the proposed method.

Efficient dimension-by-dimension higher order finite-volume methods for a Cartesian grid with cell-based refinement

Abstract A new higher-order scheme for hyperbolic systems of conservation law on Cartesian grids with cell-based refinement is proposed. The scheme is based on the finite volume methods, which admits a simple formulation around the hanging-nodes. Dimension-by-dimension reconstruction is applied to utilize the advantage of Cartesian grids. A quadrature modification flux (QMF) is introduced, which modifies the second-order error term of the flux integration over the cell-interface. The QMF can be evaluated using the state variables and the first derivatives stored in the face-left and right cells. There is no need to calculate the point-value or to use multi-points flux quadrature. In addition, a two-step reconstruction method is introduced to achieve a higher-order reconstructed value. The scheme achieves fourth-order accuracy where the grids are locally uniform, and retains second-order accuracy around the hanging-nodes. The accuracy and efficiency of the scheme is demonstrated in some example problems: inviscid vortex advection, Shu–Osher problem, double Mach reflection, and transonic flow around the NACA 0012 airfoil. The present scheme is demonstrated to function stably and consistently.

A two-step filtering-based iterative image reconstruction method for interior tomography.

The optimization-based method that utilizes the additional sparse prior of region-of-interest (ROI) image, such as total variation, has been the subject of considerable research in problems of interior tomography reconstruction. One challenge for optimization-based iterative ROI image reconstruction is to build the relationship between ROI image and truncated projection data. When the reconstruction support region is smaller than the original object, an unsuitable representation of data fidelity may lead to bright truncation artifacts in the boundary region of field of view. In this work, we aim to develop an iterative reconstruction method to suppress the truncation artifacts and improve the image quality for direct ROI image reconstruction. A novel reconstruction approach is proposed based on an optimization problem involving a two-step filtering-based data fidelity. Data filtering is achieved in two steps: the first takes the derivative of projection data; in the second step, Hilbert filtering is applied in the differentiated data. Numerical simulations and real data reconstructions have been conducted to validate the new reconstruction method. Both qualitative and quantitative results indicate that, as theoretically expected, the proposed method brings reasonable performance in suppressing truncation artifacts and preserving detailed features. The presented local reconstruction method based on the two-step filtering strategy provides a simple and efficient approach for the iterative reconstruction from truncated projections.

Three-dimensional reconstruction of the lower limb from biplanar calibrated radiographs

Three-dimensional (3D) reconstruction of lower limbs is essential for surgical planning and clinical outcome evaluation. 3D reconstruction from biplanar calibrated radiographs may be an alternative to irradiation issues of CT-scan. A previous study proposed a two-step reconstruction method based on parametric models and statistical inferences leading to a fast Initial Solution (IS) followed by manual adjustments. This study aims to improve the IS using a new 3D database, a novel parametric model of the tibia and a different regression approach. The IS was evaluated in terms of shape accuracy on 9 lower limbs and reproducibility of clinical measurements on 22 lower limbs. Reconstruction time was also evaluated. Comparison to the previous method showed an improvement of the IS in terms of shape accuracy (1.3 vs. 1.6 and 2mm respectively for both femur and tibia) and reproducibility of clinical measurements (i.e. 3.1° vs. 8.3° for neck-shaft-angle; 4.2° and 5° vs. 5° and 6° for tibial and femoral torsion respectively). The proposed approach constitutes a considerable step towards an automatic 3D reconstruction of lower limb.

Two-step reconstruction method using global optimization and conjugate gradient for ultrasound-guided diffuse optical tomography

Ultrasound-guided diffuse optical tomography (DOT) is a promising method for characterizing malignant and benign lesions in the female breast. We introduce a new two-step algorithm for DOT inversion in which the optical parameters are estimated with the global optimization method, genetic algorithm. The estimation result is applied as an initial guess to the conjugate gradient (CG) optimization method to obtain the absorption and scattering distributions simultaneously. Simulations and phantom experiments have shown that the maximum absorption and reduced scattering coefficients are reconstructed with less than 10% and 25% errors, respectively. This is in contrast with the CG method alone, which generates about 20% error for the absorption coefficient and does not accurately recover the scattering distribution. A new measure of scattering contrast has been introduced to characterize benign and malignant breast lesions. The results of 16 clinical cases reconstructed with the two-step method demonstrates that, on average, the absorption coefficient and scattering contrast of malignant lesions are about 1.8 and 3.32 times higher than the benign cases, respectively.

Reconstructing missing daily precipitation data using regression trees and artificial neural networks for SWAT streamflow simulation

Environmental models typically require a complete time series of meteorological inputs, thus reconstructing missing data is a key issue in the functionality of such physical models. The objective of this work was to develop a new technique to reconstruct missing daily precipitation data in the central part of Chesapeake Bay Watershed using a two-step reconstruction method (RT + ANN) that employed artificial neural networks (ANN) with inputs only from stations that were found to be influential in bootstrap applications of regression trees (RT). The predictive performance of RT + ANN was also compared with those of stand-alone RT and ANN methods. In addition to statistical comparisons of the reconstructed precipitation time series, these resulting data in the Soil and Water Assessment Tool (SWAT) watershed model were used to perform an error propagation analysis in streamflow simulations. The RT provided a transparent visual representation of the similarity between the stations in their daily precipitation time series. Seven years of data from 39 weather stations showed that both RT and ANN provided the reconstruction accuracy comparable to (or better than) published earlier results of precipitation reconstruction. The RT + ANN method significantly improved accuracy and was more robust when compared to RT or ANN methods. This method also provided more accurate and robust SWAT streamflow predictions with reconstructed precipitation.

Exact reconstruction in photoacoustic tomography with circular integrating detectors II: Spherical geometry

Illuminating tissue with pulsed electromagnetic waves generates acoustic waves inside an object which can be measured and converted into a three-dimensional (3d) image. This text is concerned with a two-step reconstruction method where the acoustic pressure is measured with circular integrating detectors. In the first step, reconstruction formulas for some kind of projection of the source distribution are derived; in the second step, an inversion formula for a circular radon transform on the sphere is developed. Copyright © 2010 John Wiley & Sons, Ltd.

Phase-contrast diffuse optical tomography for in vivo breast imaging: a two-step method

We present a two-step reconstruction method that can qualitatively and quantitatively improve the reconstruction of tissue refractive index (RI) distribution by phase-contrast diffuse optical tomography (PCDOT). In this two-step method, we first recover the distribution of tissue absorption and scattering coefficients by conventional diffuse optical tomography to obtain the geometrical information of lesions, allowing the incorporation of geometrical information as a priori in the PCDOT reconstruction using a locally refined mesh. The method is validated by a series of phantom experiments and evaluated using in vivo data from 42 human subjects. The results demonstrate clear contrast of RI between the lesion and the surroundings, making the image interpretation straightforward. The sensitivity and specificity from these 42 cases are both 81% when RI is used as an imaging parameter for distinguishing between malignant and benign lesions.

Quantitative reconstruction of refractive index distribution and imaging of glucose concentration by using diffusing light

We show that a two-step reconstruction method can be adapted to improve the quantitative accuracy of the refractive index reconstruction in phase-contrast diffuse optical tomography (PCDOT). We also describe the possibility of imaging tissue glucose concentration with PCDOT. In this two-step method, we first use our existing finite-element reconstruction algorithm to recover the position and shape of a target. We then use the position and size of the target as a priori information to reconstruct a single value of the refractive index within the target and background regions using a region reconstruction method. Due to the extremely low contrast available in the refractive index reconstruction, we incorporate a data normalization scheme into the two-step reconstruction to combat the associated low signal-to-noise ratio. Through a series of phantom experiments we find that this two-step reconstruction method can considerably improve the quantitative accuracy of the refractive index reconstruction. The results show that the relative error of the reconstructed refractive index is reduced from 20% to within 1.5%. We also demonstrate the possibility of PCDOT for recovering glucose concentration using these phantom experiments.

Complex-wave retrieval from a single off-axis hologram.

We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data sets and demonstrate its applicability to real-world experimental conditions by reconstructing optically acquired holograms.