Reconstruction Scheme Research Articles

Investigating the effects of numerical algorithms on global magnetohydrodynamics simulations of solar wind in the inner heliosphere

This paper explores the effects of numerical algorithms on global magnetohydrodynamics simulations of solar wind (SW) in the inner heliosphere. To do so, we use sunRunner3D, a 3-D magnetohydrodynamics model that employs the boundary conditions generated by CORHEL and the PLUTO code to compute the plasma properties of the SW with the ideal magnetohydrodynamics approximation up to 1.1 AU in the inner heliosphere. Mainly, we define three different combinations of numerical algorithms based on their diffusion level. This diffusion level is related to the way of solving the magnetohydrodynamics equations using the finite volume formulation, and, therefore, we set in terms of the divergence-free condition methods, Riemann solvers, variable reconstruction schemes, limiters, and time-steeping algorithms. According to the simulation results, we demonstrate that sunRunner3D reproduces global features of Corotating Interaction Regions observed by Earth-based spacecraft for a set of Carrington rotations that cover a period that lays in the late declining phase of solar cycle 24, independently of the numerical algorithms. Moreover, statistical analyses between models and in-situ measurements show reasonable agreement with the observations, and remarkably, the high diffusive method matches better with in-situ data than low diffusive methods.

The kinetic energy transfer analysis between the gas and the liquid in flow-focusing of the micro-jet

The present study uses computational fluid dynamics to analyse the kinetic energy transfer from the gas to the liquid phase, considering the significant influence of surface tension. The considered situation is the gas dynamic virtual nozzle, where the co-flowing gas focuses and accelerates the liquid jet. The experimentally validated half-space three-dimensional gas-liquid mixture model addresses the unsteady, incompressible, isothermal, Newtonian, low-turbulent two-phase flow. The continuity, momentum and the k-ω SST turbulence model are employed to resolve the fluid flow. The numerical solution is based on the finite volume method and volume of fluid approach with a geometric reconstruction scheme for tracking the gas-liquid interface. The total pressure of the gas, an indication of its energy, is tracked along streamlines and analysed spatially and temporarily. It is found that around 50 % of the focusing gas energy is transferred to the liquid jet before its breakup for the nozzle with Weber number 3.5, and gas and jet Reynolds number 1842 and 108, respectively. The linear regression between jet length and energy transfer efficiency is discovered. The presented methodology represents an essential tool for analysing and understanding the energy transfer process between the focusing gas and the liquid jet.

KFVM-WENO: A High-order Accurate Kernel-based Finite Volume Method for Compressible Hydrodynamics

This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Nonoscillatory reconstruction is achieved through an adaptive-order weighted essentially nonoscillatory (WENO) method cast into a form suited to multidimensional reconstruction. A kernel-based approach inspired by radial basis functions and Gaussian process modeling, which we call kernel-based finite volume method with WENO, is presented here. This approach allows the creation of a scheme of arbitrary order of accuracy with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows for a more straightforward extension to higher spatial dimensions and removes the need for complicated boundary conditions on intermediate quantities in modified dimension-by-dimension methods. In addition, a new simple yet effective set of reconstruction variables is introduced, which could be useful in existing schemes with little modification. The proposed scheme is applied to a suite of stringent and informative benchmark problems to demonstrate its efficacy and utility. A highly parallel multi-GPU implementation using Kokkos and the message-passing interface is also provided.

Image fast reconstruction for sparse view computed tomography with reduced sampling integration time

Industrial computed tomography (CT) can detect the internal structure of objects nondestructively. Its scanning and image reconstruction are time-consuming, which limits its application in the fast detection field. In this work, we reduce the sampling integration time in sparse view CT to achieve ultra-fast scanning in only 5 s. However, this ultra-fast scanning method produces more noise and streak artifacts in the reconstructed CT images. The existing reconstruction methods cannot effectively reconstruct high quality CT images under this ultra-fast scanning. To solve this issue, a faster and higher quality CT image reconstruction method is proposed in this paper. We construct a novel objective function using multi-directional TV and adaptive non-local means (ANLM), and design a solution algorithm to solve the objective function. The multi-directional TV-norm takes into account the differences in horizontal, vertical, and 45° directional gradients to obtain more image detail information, while the ANLM-norm focuses on noise suppression. Simulation and practical experiments show that the proposed method can reconstruct higher quality CT images under faster CT scanning strategy, and the peak signal to noise ratio (PSNR) is 1.3 dB higher than the optimal baseline algorithm. On the other hand, our method converges faster and achieves a shorter CT image reconstruction time, which is 47 s shorter than the current popular iterative reconstruction methods. This reconstruction method provides a reliable scheme for faster CT scanning and image reconstruction.

Numerical investigation of aerodynamic interactions for the coaxial rotor system in low-speed forward flight

This study is conducted to investigate the aerodynamic characteristics of a coaxial rotor in low-speed forward flight using a high-fidelity computational fluid dynamics (CFD) solver. Numerical simulations are performed on the coaxial rotor and its isolated upper and lower rotors at two small advance ratios, 0.12 and 0.24. Interaction events in the flowfield, especially blade-vortex-interaction (BVI), are studied in detail. As the forward speed increases, the airload distributions become concentrated on the front part of the disk. Fluctuations in the loading indicate self-BVIs within each rotor, and blade-crossover events and rotor-to-rotor BVIs between the coaxial upper and lower rotors. Principal BVI events are identified in the well-captured wake structures by the 8th-order TENO reconstruction scheme. Self-BVIs on all rotors reduce in strength as the forward speed increases, while rotor-to-rotor BVIs on the coaxial lower rotor increase in strength with the increasing forward speed. In the coaxial configuration, the wake of the upper rotor is induced to move backwards and downwards due to the exertion of the lower rotor wake. The wake of the coaxial lower rotor features the most complex flow nature among all rotors. At both advance ratios, the coaxial lower rotor experiences a parallel rotor-to-rotor BVI, causing highly impulsive loading fluctuations along the blade span.

Cosmological aspects of the unimodular-mimetic [formula omitted] gravity

In this work, we introduce and study the unimodular-mimetic f(G) gravity, where unimodular and mimetic constraints are incorporated through corresponding Lagrange multipliers. We present field equations governing this theory and discuss their main properties. According to that, the mimetic constraint is provided via the pressureless matter, while the unimodular constraint yields cosmological constant in a natural manner. By using the reconstruction scheme, we obtain quadratic unimodular-mimetic f(G)=AG2 gravity capable of describing hybrid expansion law and the power law evolution. Furthermore, we employ an inverted reconstruction technique in order to derive specific f(G) function that reproduces the Hubble rate of symmetric bounce. The unimodular-mimetic f(G)=AG2 is also shown to be compatible with the BICEP2/Keck and Planck data. To this end, we incorporate updated constraints on the scalar-to-tensor ratio and spectral index, utilizing a perfect fluid approach to the slow-roll parameters. Through an analysis of that kind, we demonstrate that the theoretical framework presented here can indeed characterize inflation that agrees with the observational findings. Consequently, the introduced extension appears to have potential to describe and encompass a wide spectrum of cosmological models.

Semi-discrete entropy-preserving surface reconstruction schemes for the shallow water equations: Analysis of physical structures

We aim to introduce a new variant of hydrostatic reconstruction scheme, which is physical-structure-preserving and semi-discrete entropy-preserving for shallow water equations with a discontinuous bottom topography, based on novel surface reconstructions (NSR). The NSR is used to define approximate Riemann states with respect to the water depth and the velocity to compute consistent numerical fluxes across the cell interface and the upwind interface source term. This work is motivated by path-conservative surface reconstructions (Dong (2023) [19]), in which the conditions to satisfy the entropy inequality are complicated. We propose the NSR scheme to satisfy the entropy inequality without the corresponding complicated conditions. A key advantage of the NSR scheme is to preserve the physical structure of the water surface in the sense that when the water surface is continuous, then the defined approximate Riemann state should inherit this property. The physical-structure-preserving property is indispensable for obtaining a more accurate discretized source term and avoiding artificial “waterfall” effects. We prove that the NSR scheme satisfies a semi-discrete entropy condition and can guarantee the water depth to be nonnegative, and maintain the stationary state. We show several computed results to compare the NSR scheme with the hydrostatic reconstruction scheme based on subcell reconstructions and the path-conservative surface reconstruction scheme. We also extend the NSR scheme for pollutant transport in shallow water based on adaptive moving triangular meshes. Finally, several numerical results obtained by the adaptive NSR scheme for pollutant transport in shallow water are shown.

High-order genuinely multidimensional finite volume methods via kernel-based WENO

In this paper a family of fully multidimensional kernel-based reconstruction schemes for use in finite volume methods (FVMs) will be presented. These methods are intended for use in shock dominated problems, and stability is achieved through a suitable adaptation of the Adaptive Order Weighted Essentially Non-Oscillatory (WENO-AO) method to the proposed kernel-based reconstruction schemes. There are a number of key difficulties in the design of high-order finite volume schemes which will be discussed and addressed. High (4th and 6th) order convergence will be demonstrated on smooth exact solutions of the ideal MHD equations. The very same scheme will then be applied to extremely stringent astrophysical benchmark problems.

Artifact-suppressing reconstruction of strongly interacting objects in X-ray near-field holography without a spatial support constraint.

The phase problem is a well known ill-posed reconstruction problem of coherent lens-less microscopic imaging, where only the squared magnitude of a complex wavefront is measured by a detector while the phase information of the wave field is lost. To retrieve the lost information, common algorithms rely either on multiple data acquisitions under varying measurement conditions or on the application of strong constraints such as a spatial support. In X-ray near-field holography, however, these methods are rendered impractical in the setting of time sensitive in situ and operando measurements. In this paper, we will forego the spatial support constraint and propose a projected gradient descent (PGD) based reconstruction scheme in combination with proper preprocessing and regularization that significantly reduces artifacts for refractive reconstructions from only a single acquired hologram without a spatial support constraint. We demonstrate the feasibility and robustness of our approach on different data sets obtained at the nano imaging endstation of P05 at PETRA III (DESY, Hamburg) operated by Helmholtz-Zentrum Hereon.

Research on Image Processing Resource Reconstruction Based on Load Balancing Strategy

With the development of intelligent vehicles, the vehicle image processing system has put forward increasing demand for computing resource utilization efficiency and real-time processing. However, the traditional information processing method that binds software and hardware severely restricts the efficient use of image processing resources. In order to solve this problem, this paper proposes a resource reconstruction scheme based on a load balancing strategy, which can realize unified management and dynamic allocation of image processing resources by establishing a system resource view. Then, this paper builds a physical verification platform and constructs a comparative verification experiment to verify the effectiveness of the resource reconstruction scheme. Experimental results prove that this resource reconstruction scheme can effectively improve the resource utilization efficiency of multi-core digital signal processing (DSP), realize software-defined hardware functions, and optimize the real-time performance of parallel processing.

Influence of the Emitter Shape on the Field-of-View in Atom Probe Tomography.

Atom probe tomography (APT) is a unique analytical technique that offers three-dimensional elemental mapping with a spatial resolution down to the sub-nanometer. When APT is applied on complex heterogenous systems and/or under certain experimental conditions, that is, laser illumination, the specimen shape can deviate from an ideal hemisphere. Insufficient consideration of this aspect can introduce artifacts in the reconstructed dataset, ultimately degrading its spatial accuracy. So far, there has been limited investigation into the detailed evolution of emitter shape and its impact on the field-of-view (FOV). In this study, we numerically and experimentally investigated the FOV for asymmetric emitters and its evolution throughout the analysis depth. Our analysis revealed that, for asymmetric emitters, the ions evaporated from the topmost region of the specimen (summit) project approximately to the detector center. Furthermore, we demonstrated the implications of this finding on the FOV location for asymmetric emitters. Based on our findings, the location of the center of the FOV can deviate from the specimen central axis with an evolution depending on the evolution of the emitter shape. This study highlights the importance of accounting for the specimen shape when developing advanced data reconstruction schemes to enhance spatial resolution and accuracy.

Bayesian view on the training of invertible residual networks for solving linear inverse problems *

Learning-based methods for inverse problems, adapting to the data’s inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works address the issue of theoretical guarantees. Recently, Arndt et al (2023 Inverse Problems 39 125018) exploited invertible residual networks (iResNets) to learn provably convergent regularizations given reasonable assumptions. They enforced these guarantees by approximating the linear forward operator with an iResNet. Supervised training on relevant samples introduces data dependency into the approach. An open question in this context is to which extent the data’s inherent structure influences the training outcome, i.e. the learned reconstruction scheme. Here, we address this delicate interplay of training design and data dependency from a Bayesian perspective and shed light on opportunities and limitations. We resolve these limitations by analyzing reconstruction-based training of the inverses of iResNets, where we show that this optimization strategy introduces a level of data-dependency that cannot be achieved by approximation training. We further provide and discuss a series of numerical experiments underpinning and extending the theoretical findings.

Analysis of the interaction of a shock with two square bubbles containing different gases

The shock–bubble interaction problem remains of interest to researchers to study shock accelerated in-homogeneous flows and the Richtmyer–Meshkov instability. In the present work, simulations have been performed using the high-order Direct Flux Reconstruction scheme to study such interactions when a Mach 1.22 shock is incident on two configurations: one in which a helium bubble is in front of SF6, and, the other in which SF6 is in front of helium; in both cases, the ambient gas is nitrogen. High-order schemes are often preferred for such cases since these interactions usually involve small-scale flow features that are better resolved using high-order methods. When helium is in front of SF6, the helium bubble traverses along the initial horizontal surface of the SF6 and nitrogen, and with time, moves ahead of SF6. There are no regions of pure helium for this case at later stages. When SF6 is placed in front of helium, a separation of helium takes place in two parts, one of which mixes with SF6 while the other remains mostly pure even at later stages. A jet of nitrogen can also be seen moving at very high speeds, penetrating the region of pure helium.

Spatial Transformation Accelerator with Parallel Data Access Scheme for Sample Reconstruction

Spatial image transformation is a commonly used component in many image processing pipelines. It enables the correction of optical distortions, image registration onto a common reference plane, electronic image stabilisation, digital zoom, video mosaicking, etc. With the growing tendency to embed image processing in low-power devices, attaining an efficient transformation solution becomes increasingly decisive. Furthermore, interpolation is the key operation in achieving the high quality of the transformed data from the original data. Fortunately, different implementations have already seen several efficiency improvements in recent years. However, interpolation relies on sampling a set of neighbouring points from memory, which has yet to be addressed efficiently for smaller computational platforms with limited memory resources. In this work, we derive a generic mathematical model and circuit design principles for the spatial transformation accelerator design for N-dimensional data. Furthermore, we present an efficient simultaneous access scheme for high-quality signal reconstruction. Finally, the introduced ideas are verified in field programmable gate arrays using one-dimensional and two-dimensional data transformation use cases. The presented solution is able to transform images with sizes ranging from 256 × 256 to 8192 × 8192 and achieves a transfer rate of 275 frames per second with 512 × 512 images.

PNMC: Four-dimensional conebeam CT reconstruction combining prior network and motion compensation

Four-dimensional conebeam computed tomography (4D CBCT) is an efficient technique to overcome motion artifacts caused by organ motion during breathing. 4D CBCT reconstruction in a single scan usually divides projections into different groups of sparsely sampled data based on the respiratory phases. The reconstructed images within each group present poor image quality due to the limited number of projections. To improve the image quality of 4D CBCT in a single scan, we propose a novel reconstruction scheme that combines prior knowledge with motion compensation. We apply the reconstructed images of the full projections within a single routine as prior knowledge, providing structural information for the network to enhance the restoration structure. The prior network (PN-Net) is proposed to extract features of prior knowledge and fuse them with the sparsely sampled data using an attention mechanism. The prior knowledge guides the reconstruction process to restore the approximate organ structure and alleviates severe streaking artifacts. The deformation vector field (DVF) extracted using deformable image registration among different phases is then applied in the motion-compensated ordered-subset simultaneous algebraic reconstruction algorithm to generate 4D CBCT images. Proposed method has been evaluated using simulated and clinical datasets and has shown promising results by comparative experiment. Compared with previous methods, our approach exhibits significant improvements across various evaluation metrics.

Cosmology of unimodular Born–Infeld-[formula omitted] gravity

We propose a novel modified gravity: unimodular generalization of the Born–Infeld-f(R) gravity within the framework of cosmology. After formulating the action corresponding to the generalized Born–Infeld-f(R) gravity, we present a reconstruction scheme of this unimodular extension to achieve various cosmological eras of the universe. Interestingly, the unimodular generalization of Born–Infeld-f(R) gravity proves to be suitable for inflation (de-Sitter and quasi de-Sitter) along with power law cosmology which actually includes from reheating to the Standard Big-Bang cosmology. Apart from the inflation, such generalized Born–Infeld-f(R) theory is also capable to trigger non-singular bouncing cosmology for suitable forms of the unimodular Lagrange multiplier, which are exotic for the standard Einstein–Hilbert gravity and cannot be realized in that case. The possible consequences are discussed.

Cosmology of Tsallis and Kaniadakis holographic dark energy in Saez–Ballester theory and consideration of viscous van der Waals fluid

In the framework of Saez–Ballester (SB) theory, the current study proposes a reconstruction scheme for Tsallis and Kaniadakis holographic dark energy, particular cases of a more generalised Nojiri–Odintsov holographic dark energy (Nojiri and Odintsov, 2006; The European Physical Journal C, 2017, 77, pp.1-8.), with Hubble horizon and future event horizons serving as the universe’s respective trapping horizons. The Hubble parameter was rebuilt by placing a constraint on the metric potential inside the conservation equation. As a result, the holographic dark energy of Tsallis and Kaniadakis are recreated, and the cosmology and thermodynamics are examined. Lastly, an interacting van der Waals (VDW) coupled fluid model was examined in the context of bulk viscosity, and the behaviour of the equation of state (EoS) parameter was examined.

Deep learning framework for three-dimensional surface reconstruction of object of interest in photoacoustic tomography.

Photoacoustic tomography (PAT) is a non-ionizing hybrid imaging technology of clinical importance that combines the high contrast of optical imaging with the high penetration of ultrasonic imaging. Two-dimensional (2D) tomographic images can only provide the cross-sectional structure of the imaging target rather than its overall spatial morphology. This work proposes a deep learning framework for reconstructing three-dimensional (3D) surface of an object of interest from a series of 2D images. It achieves end-to-end mapping from a series of 2D images to a 3D image, visually displaying the overall morphology of the object. The framework consists of four modules: segmentation module, point cloud generation module, point cloud completion module, and mesh conversion module, which respectively implement the tasks of segmenting a region of interest, generating a sparse point cloud, completing sparse point cloud and reconstructing 3D surface. The network model is trained on simulation data sets and verified on simulation, phantom, and in vivo data sets. The results showed superior 3D reconstruction performance both visually and on the basis of quantitative evaluation metrics compared to the state-of-the-art non-learning and learning approaches. This method potentially enables high-precision 3D surface reconstruction from the tomographic images output by the preclinical PAT system without changing the imaging system. It provides a general deep learning scheme for 3D reconstruction from tomographic scanning data.

Joint Dataset Reconstruction and Power Control for Distributed Training in D2D Edge Network

The intrinsic nature of non-independent and identically distributed datasets on heterogeneous devices slows down the distributed model training process and reduces the training accuracy. To settle this problem, we propose a dataset reconstruction scheme to transform the data distribution of training device’s dataset into independent and identically distributed dataset via data exchange among trusted devices. For energy efficiency, we further consider power control for the devices. We then formulate an optimization problem, which is a mixed integer non-linear programming problem, to minimize the total energy consumption for each round of distributed training. Due to the NP-hardness and coupling property of the optimization problem, we decompose it into two subproblems for dataset reconstruction and power control, respectively. An approximation algorithm is designed to obtain a near-optimal auxiliary devices set for dataset reconstruction with minimum energy consumption, while meeting the variance constraint of the optimization problem. We prove that approximation algorithm has a worst-case approximation ratio of 1+ln|Ωi(t)|, where |Ωi(t)| is the required data samples for dataset reconstruction of each training device. For power control, we design a dynamic programming algorithm to further reduce the energy consumption. For comparison, we propose three benchmark schemes that adopt either one of the algorithms or neither. We also customize three baseline algorithms based on the state-of-the-arts to compare with our proposed algorithm. Numerical results show that, our proposed algorithm outperforms three benchmarks on the average energy consumption for one round for different cases. When varying the labels that each device owns, our proposed algorithm outperforms the other three baseline algorithms on training accuracy. Besides, when setting a target accuracy, our proposed algorithm always has the lowest energy consumption.

Analytical corrections for B1-inhomogeneity and signal decay in multi-slice 2D spiral hyperpolarized 129Xe MRI using keyhole reconstruction.

Hyperpolarized xenon MRI suffers from heterogeneous coil bias and magnetization decay that obscure pulmonary abnormalities. Non-physiological signal variability can be mitigated by measuring and mapping the nominal flip angle, and by rescaling the images to correct for signal bias and decay. While flip angle maps can be calculated from sequentially acquired images, scan time and breath-hold duration are doubled. Here, we exploit the low-frequency oversampling of 2D-spiral and keyhole reconstruction to measure flip angle maps from a single acquisition. Flip angle maps were calculated from two images generated from a single dataset using keyhole reconstructions and a Bloch-equation-based model suitable for hyperpolarized substances. Artifacts resulting from acquisition and reconstruction schemes (e.g., keyhole reconstruction radius, slice-selection profile, spiral-ordering, and oversampling) were assessed using point-spread functions. Simulated flip angle maps generated using keyhole reconstruction were compared against the paired-image approach using RMS error (RMSE). Finally, feasibility was demonstrated for in vivo xenon ventilation imaging. Simulations demonstrated accurate flip angle maps and B1-inhomogeneity correction can be generated with only 1.25-fold central-oversampling and keyhole reconstruction radius = 5% (RMSE = 0.460°). These settings also generated accurate flip angle maps in a healthy control (RSME = 0.337°) and a person with cystic fibrosis (RMSE = 0.404°) in as little as 3.3 s. Regional lung ventilation images with reduced impact of B1-inhomogeneity can be acquired rapidly by combining 2D-spiral acquisition, Bloch-equation-based modeling, and keyhole reconstruction. This approach will be especially useful for breath-hold studies where short scan durations are necessary, such as dynamic imaging and applications in children or people with severely compromised respiratory function.