Linear Reconstruction Techniques Research Articles

Ultrasonic computed tomography-based internal-defect detection and location of underwater concrete piers

Concrete piers are the key load-bearing components of wading bridges. Most detection equipment and methods focus on the surface defects of underwater piers, whereas the detection methods of internal defects are very deficient. This study proposes an ultrasonic computed tomography method combining linear travel time interpolation and simultaneous iterative reconstruction techniques for detecting internal defects in underwater concrete piers. The two-dimensional median filtering and self-organizing feature map are utilized to post-process tomographic images and the confidence approach is employed to detect defects. The efficacy of the proposed method is validated through numerical simulation and underwater experiments, respectively. The Comsol Multiphysics is utilized to simulate the two-dimensional random aggregate model of the concrete and internal defects are added to validate the method’s effectiveness from a mesoscopic perspective. Then actual scale piers containing embedded defects are cast and detected. The results demonstrate that the method can identify and locate internal defects in numerical simulations and practical tests. The numerical simulation experiments results are superior to those of scale concrete specimens. In addition, underwater concrete piers with larger internal defects, square holes, and no steel reinforcements tend to have better detection results.

Nonlinear Wave Front Reconstruction from a Pyramid Sensor using Neural Networks

The pyramid wave front sensor (PyWFS) has become increasingly popular to use in adaptive optics (AO) systems due to its high sensitivity. The main drawback of the PyWFS is that it is inherently nonlinear, which means that classic linear wave front reconstruction techniques face a significant reduction in performance at high wave front errors, particularly when the pyramid is unmodulated. In this paper, we consider the potential use of neural networks (NNs) to replace the widely used matrix vector multiplication (MVM) control. We aim to test the hypothesis that the NN's ability to model nonlinearities will give it a distinct advantage over MVM control. We compare the performance of a MVM linear reconstructor against a dense NN, using daytime data acquired on the Subaru Coronagraphic Extreme Adaptive Optics system (SCExAO) instrument. In a first set of experiments, we produce wavefronts generated from 14 Zernike modes and the PyWFS responses at different modulation radii (25, 50, 75, and 100 mas). We find that the NN allows for a far more precise wave front reconstruction at all modulations, with differences in performance increasing in the regime where the PyWFS nonlinearity becomes significant. In a second set of experiments, we generate a data set of atmosphere-like wavefronts, and confirm that the NN outperforms the linear reconstructor. The SCExAO real-time computer software is used as baseline for the latter. These results suggest that NNs are well positioned to improve upon linear reconstructors and stand to bring about a leap forward in AO performance in the near future.

EP06.20: Can 3D linear reconstruction technique be used for the assessment of the brainstem‐vermis angle?

EP06.20: Can 3D linear reconstruction technique be used for the assessment of the brainstem‐vermis angle?

Visualization of the distortion induced by nonlinear noise reduction in computed tomography.

We developed a method to visualize the image distortion induced by nonlinear noise reduction algorithms in computed tomography (CT) systems. Nonlinear distortion was defined as the induced residual when testing a reconstruction algorithm by the criteria for a linear system. Two types of images were developed: a nonlinear distortion of an object () image and a nonlinear distortion of noise () image to visualize the nonlinear distortion induced by an algorithm. Calculation of the images requires access to the sinogram data, which is seldomly fully provided. Hence, an approximation of the image was estimated. Using simulated CT acquisitions, four noise levels were added onto forward projected sinograms of a typical CT image; these were noise reduced using a median filter with the simultaneous iterative reconstruction technique or a total variation filter with the conjugate gradient least-squares algorithm. The linear reconstruction technique filtered back-projection was also analyzed for comparison. Structures in the image indicated contrast and resolution reduction of the nonlinear denoising. Although the approximated image represented the original image well, it had a higher random uncertainty. The image for the median filter indicated both stochastic variations and structures reminding of the object while for the total variation filter only stochastic variations were indicated. The developed images visualize nonlinear distortions of denoising algorithms. The object may be distorted by the noise and vice versa. Analyzing the distortion correlated to the object is more critical than analyzing a distortion of stochastic variations. The absence of nonlinear distortion may measure the robustness of the denoising algorithm.

Effect of Reverberation on Neural Responses to Natural Speech in Rabbit Auditory Midbrain: No Evidence for a Neural Dereverberation Mechanism.

Reverberation is ubiquitous in everyday acoustic environments. It degrades both binaural cues and the envelope modulations of sounds and thus can impair speech perception. Still, both humans and animals can accurately perceive reverberant stimuli in most everyday settings. Previous neurophysiological and perceptual studies have suggested the existence of neural mechanisms that partially compensate for the effects of reverberation. However, these studies were limited by their use of either highly simplified stimuli or rudimentary reverberation simulations. To further characterize how reverberant stimuli are processed by the auditory system, we recorded single-unit (SU) and multiunit (MU) activity from the inferior colliculus (IC) of unanesthetized rabbits in response to natural speech utterances presented with no reverberation ("dry") and in various degrees of simulated reverberation (direct-to-reverberant energy ratios (DRRs) ranging from 9.4 to -8.2 dB). Linear stimulus reconstruction techniques (Mesgarani et al., 2009) were used to quantify the amount of speech information available in the responses of neural ensembles. We found that high-quality spectrogram reconstructions could be obtained for dry speech and in moderate reverberation from ensembles of 25 units. However, spectrogram reconstruction quality deteriorated in severe reverberation for both MUs and SUs such that the neural degradation paralleled the degradation in the stimulus spectrogram. Furthermore, spectrograms reconstructed from responses to reverberant stimuli resembled spectrograms of reverberant speech better than spectrograms of dry speech. Overall, the results provide no evidence for a dereverberation mechanism in neural responses from the rabbit IC when studied with linear reconstruction techniques.

Portfolio selection of power generation projects considering the synergy of project and uncertainty of decision information

Specifying which projects to be invested in under constraints can improve the investment efficiency of enterprise. The article studies on portfolio selection of power generation projects, considering the synergy between a pair of projects and the uncertainty of decision information. Firstly, objectives and constraints for generation power project portfolio are defined by economy, environment and society-three aspects. Synergies between each pair of projects are calculated in resource, management, technology and operation, and adopted into objective in a form of comprehensive synergy. In the process of model solution, fuzzy number is employed to describe the information of alternative projects to enhance the accuracy of decision. Linear reconstruction technique is introduced to equally transform the non-linear planning model into a linear 0–1 problem, reducing the difficulty of solving the model. Through a case study, the feasibility and operability of project portfolio selection (PPS) framework constructed in article are verified. The results show that comprehensive benefit of project portfolio considering the synergy is 8.999, which is significantly higher than the model without synergy, providing convincing support to decision makers. Further, the structure of solution indicates that the current investments in coal-fired power should not be stopped arbitrarily, and different types of power generation projects need to be developed in balance. The research can provide a reference in ideas and models to the investor in multi-project investment decision-making.

An accuracy comparison of piecewise linear reconstruction techniques for the characteristic finite volume method for two‐dimensional convection‐diffusion equation

AbstractIn this paper, we apply the characteristic finite volume method (CFVM) for solving a convection‐diffusion problem on two‐dimensional triangular grids. The finite volume method is used to discretize the equation while the finite element method is applied to estimate the gradient quantities at cell faces. The numerical analysis of the convergence has been implemented for the CFVM in one‐dimension. The approximate L2 norm of the error is derived to determine the errors for the approximate solution. The accuracy of four piecewise linear reconstruction techniques, namely, Frink, Holmes‐Connell, Green‐Gauss, and least‐squares methods are investigated on structured triangular grids. Numerical evidence shows that the least‐squares method is the most accurate of all methods for smooth initial condition problems. For discontinuous initial condition problems, the Frink and the Holmes‐Connell methods give a spurious oscillating solution in the vicinity of the discontinuity upstream of the discontinuity, and the Green‐Gauss and least‐squares methods give a spurious oscillating solution in the vicinity of the discontinuity downstream of the discontinuity. Moreover, the amplitude of the oscillation could be amplified on the finer grid sizes.

A signal detection model for quantifying overregularization in nonlinear image reconstruction.

Many useful image quality metrics for evaluating linear image reconstruction techniques do not apply to or are difficult to interpret for nonlinear image reconstruction. The vast majority of metrics employed for evaluating nonlinear image reconstruction are based on some form of global image fidelity, such as image root mean square error (RMSE). Use of such metrics can lead to overregularization in the sense that they can favor removal of subtle details in the image. To address this shortcoming, we develop an image quality metric based on signal detection that serves as a surrogate to the qualitative loss of fine image details. The metric is demonstrated in the context of a breast CT simulation, where different equal-dose configurations are considered. The configurations differ in the number of projections acquired. Image reconstruction is performed with a nonlinear algorithm based on total variation constrained least-squares (TV-LSQ). The resulting images are studied as a function of three parameters: number of views acquired, total variation constraint value, and number of iterations. The images are evaluated visually, with image RMSE, and with the proposed signal-detection-based metric. The latter uses a small signal, and computes detectability in the sinogram and in the reconstructed image. Loss of signal detectability through the image reconstruction process is taken as a quantitative measure of loss of fine details in the image. Loss of signal detectability is seen to correlate well with the blocky or patchy appearance due to overregularization with TV-LSQ, and this trend runs counter to the image RMSE metric, which tends to favor the over-regularized images. The proposed signal detection-based metric provides an image quality assessment that is complimentary to that of image RMSE. Using the two metrics in concert may yield a useful prescription for determining CT algorithm and configuration parameters when nonlinear image reconstruction is used.

Clinical analysis of surgical treatment of post-infarction left ventricular aneurysm: a series of 254 patients

Objective: To examine the efficacy of two surgical procedures on post-infarction left ventricular aneurysm. Methods: The clinic data of 254 patients with post-infarction left ventricular aneurysm, who underwent surgical ventricular reconstruction between January 1997 and December 2019 in Department of Cardiovascular Surgery, Nanjing Hospital Affiliated to Nanjing Medical University was analyzed retrospectively. There were 183 males and 71 females aged from 31 to 81 years, with a median age of 64.6 years. Based on the size of the ventricular aneurysm, there were 73 patient received linear reconstruction (linear group) and 181 patients received endoventricular patch plasty technique (patch plasty group). Ejection fraction, left ventricular systolic and end diastolic volume and left ventricular systolic and end diastolic volume index were recorded preoperatively, 2-week, 3-month, 1-year and 5-year after operation. The survival curves were plotted with Kaplan-Meier method and the survival rates were compared by Log-rank test. Results: All patients underwent surgery with a mean cardiopulmonay bypass duration of (92±32) minutes (44 to 196 minutes) and aortic cross clamp duration of (67±22) minutes (33 to 152 minutes).There were 9 perioperative deaths with a mortality rate of 3.5%. Angina pectoris of other cases are relief and heart function improved greatly. Five years after operation, the percentage of cardiac function (New Yord Heart Association) class Ⅲ to Ⅳ patients decreased from 96.1%(244/254) to 9.9%(16/161). There was no significant difference in survival rate between linear group and patch plasty group at 1-, 3-, 5-years postoperatively (96%, 91%, 77% vs. 96%, 90%, 79%, P=0.562). Ejection fraction increased from (39±10)% (range: 22% to 50%) preoperatively to (46±6)% (range: 39% to 54%) 1-year postoperatively in the linear group, while increased from (38±13)% (range: 26% to 51%) preoperatively to (50±6)% (range: 39% to 55%) in the patch plasty group. Conclusions: Left ventricular reconstruction is quite effective for patients with post-infarction left ventricular aneurysm. The choice of operative approaches is determined by the size and range of ventricular aneurysm. Both linear reconstruction and endoventricular patch plasty technique can got similarly surgical outcomes with near and late curative effect.

On numerical simulation of flexibly supported airfoil in interaction with incompressible fluid flow using laminar–turbulence transition model

In this paper the problem of mutual interaction of the incompressible turbulent fluid flow with a flexibly supported airfoil is addressed. The problem is mathematically described with the aid of the Reynolds averaged Navier–Stokes equations. The turbulence is modeled with the aid of k-kL-ω transition model. In order to treat the motion of the domain the system of equations are written in the arbitrary Lagrangian–Eulerian. The structure motion is governed by a nonlinear system of ordinary differential equations, where two degrees of freedom for the rotation and the vertical translation are used. The problem is numerically discretized with the aid of the finite volume method using the linear reconstruction technique. The numerical results are shown.

Flood Simulation by a Well-Balanced Finite Volume Method in Tapi River Basin, Thailand, 2017

Flood simulation of a region in southern Thailand during January 2017 is presented in this work. The study area covers the Tapi river, the longest river in southern Thailand. The simulation is performed by applying the two-dimensional shallow water model in the presence of strong source terms to the local bottom topography. The model is solved numerically by our finite volume method with well-balanced property and linear reconstruction technique. This technique is accurate and efficient at solving for complex flows in the wet/dry interface problem. Measurements of flows are collected from two gauging stations in the area. The initial conditions are prepared to match the simulated flow to the measurements recorded at the gauging stations. The accuracy of the numerical simulations is demonstrated by comparing the simulated flood area to satellite images from the same period. The results are in good agreement, indicating the suitability of the shallow water model and the presented numerical method for simulating floodplain inundation.

Accelerated Simultaneous Multi-Slice MRI using Subject-Specific Convolutional Neural Networks.

Simultaneous multi-slice or multi-band (SMS/MB) imaging allows accelerated coverage in magnetic resonance imaging (MRI). Multiple slices are excited and acquired at the same time, and reconstructed using the redundancies in receiver coil arrays, similar to parallel imaging. SMS/MB reconstruction is currently performed with linear reconstruction techniques. Recently, a nonlinear reconstruction method for parallel imaging, Robust Artificial-neural-networks for k-space Interpolation (RAKI) was proposed and shown to improve upon linear methods. This method uses convolutional neural networks (CNN) trained solely on subject-specific calibration data. In this study, we sought to extend RAKI to SMS/MB imaging reconstruction. CNN training was performed on calibration data acquired prior to SMS/MB imaging, in a manner consistent with the existing linear methods. These CNNs were used to reconstruct a time series of functional MRI (fMRI) data. CNN network parameters were optimized using an extensive search of the parameter space. With these optimal parameters, RAKI substantially improves image quality compared to a commonly used linear reconstruction algorithm, especially for high acceleration rates.

Nuclear norm-based matrix regression preserving embedding for face recognition

Abstract Recently, using linear reconstruction technique to construct intrinsic graph for projection-based dimensionality reduction (DR) has aroused broad interest in face recognition. However, current methods either lack robustness to corruptions or require to perform vectorization which causes loss of local geometrical information of images. To this end, a novel nuclear norm-based matrix regression preserving embedding (NN-MRPE) method is proposed in this paper. First, NN-MRPE constructs an intrinsic graph by using the nuclear norm to evaluate the residual errors to resist data corruptions. Second, a matrix-based embedding cost function is formulated to seek two transformation matrices which can preserve the geometrical structure reflected by the intrinsic graph exactly. Finally, based on the linear regression theory, we summarize a general DR framework called linear regression preserving embedding that preserves the intrinsic structure of data by recovering the reconstruction relationship in the original space. Specifically, many existing approaches are the special cases of the linear regression preserving embedding. Experiments on five public face databases with different types of corruptions are conducted to demonstrate the efficiency of the proposed NN-MRPE method.

Constrained discriminant neighborhood embedding for high dimensional data feature extraction

When handling pattern classification problem such as face recognition and digital handwriting identification, image data is always represented to high dimensional vectors, from which discriminant features are extracted using dimensionality reduction methods. So in this paper, we present a supervised manifold learning based dimensionality reduction method named constrained discirminant neighborhood embedding (CDNE). In the proposed CDNE, on one hand, the class information of samples is taken into account to construct both an inter-class graph and an intra-class graph, where neighborhood points in the intra-class graph are selected from those with the same class and any point in the inter-class graph should sample those labeled different classes as its neighborhood points. On the other hand, locally least linear reconstruction technique is also introduced to model an objective function under the local uncorrelation constraint to explore a discriminant subspace. Compared to some related and state-of-the-art dimensionality reduction methods such as discriminant neighborhood embedding (DNE), supervised locality discriminant manifold learning (SLDML), discriminant sparse neighborhood preserving embedding (DSNPE), local graph embedding based on maximum margin criterion (LGE/MMC), uncorrelated discriminant locality preserving projection (UDLPP) and locally uncorrelated discriminant projection (LUDP), the proposed CDNE has been validated to be efficient and feasible by experimental results on some benchmark face data sets including CMU PIE, ORL and FERET.

An implicit non-staggered Cartesian grid method for incompressible viscous flows in complex geometries

A discrete forcing based Cartesian grid method is presented. The non-staggered arrangement of velocity and pressure is considered. The pressure gradient in localized discrete form is added separately with the velocity making them explicitly coupled. The governing equation is time-integrated implicitly with both linearized and non-linear forms are investigated. Both linear and bi-linear reconstruction techniques are tested for extrapolation of velocity near a complex boundary. The present method is tested for vortical flow in an inclined cavity, flow past circular and inclined square cylinder. Both homogeneous and non-homogeneous Dirichlet forcing problems are tested. The parallelized version of the method is applied to 2D-to-3D transitional flow behind a single and multiple circular cylinders. The present numerical results compare well with the previously documented results.

A novel multidimensional solution reconstruction and edge‐based limiting procedure for unstructured cell‐centered finite volumes with application to shallow water dynamics

SUMMARYOn unstructured meshes, the cell‐centered finite volume (CCFV) formulation, where the finite control volumes are the mesh elements themselves, is probably the most used formulation for numerically solving the two‐dimensional nonlinear shallow water equations and hyperbolic conservation laws in general. Within this CCFV framework, second‐order spatial accuracy is achieved with a Monotone Upstream‐centered Schemes for Conservation Laws‐type (MUSCL) linear reconstruction technique, where a novel edge‐based multidimensional limiting procedure is derived for the control of the total variation of the reconstructed field. To this end, a relatively simple, but very effective modification to a reconstruction procedure for CCFV schemes, is introduced, which takes into account geometrical characteristics of computational triangular meshes. The proposed strategy is shown not to suffer from loss of accuracy on grids with poor connectivity. We apply this reconstruction in the development of a second‐order well‐balanced Godunov‐type scheme for the simulation of unsteady two‐dimensional flows over arbitrary topography with wetting and drying on triangular meshes. Although the proposed limited reconstruction is independent from the Riemann solver used, the well‐known approximate Riemann solver of Roe is utilized to compute the numerical fluxes, whereas the Green–Gauss divergence formulation for gradient computations is implemented. Two different stencils for the Green–Gauss gradient computations are implemented and critically tested, in conjunction with the proposed limiting strategy, on various grid types, for smooth and nonsmooth flow conditions. Copyright © 2012 John Wiley & Sons, Ltd.

Fully-Coupled Modeling of Shallow Water Flow and Pollutant Transport on Unstructured Grids

Understanding the space-time dynamics of pollutant transport remains an essential impediment to accurate prediction of impacts on the ecology of rivers and coastal areas and also for establishing efficient strategies for pollution control and environmental protection. Numerical models are a powerful tool to study the water flows and pollutant transport, and recently a new generation of models is being developed to simulate the coupled flow and pollutant transport in shallow water. In this paper, a two-dimensional fully-coupled model of shallow water flows and pollutant transport was developed using a triangular unstructured grid (TIN: triangular irregular network), which is also an important module of the PIHM-Hydro modeling system. The model is based on a cell-centered upwind finite volume method using the HLL approximate Riemann solver. A multidimensional linear reconstruction technique and multi-dimensional slope limiter was implemented to achieve a second-order spatial accuracy. In order to make the model efficient and stable, an explicit-implicit method was used in temporal discretization by an operator splitting technique. A test case of the pollutant transport in a square cavity is used to validate the model. Then the model was further applied to two pollutant transport scenarios: microscale pollutant transport following dam break and mesoscale pollutant transport driven by storm surge in Galveston Bay. The numerical results show that the model could accurately predict the flow dynamics and pollutant transport in extreme events such as a dam break and a storm surge. According to the prediction of the model, the storm surge caused by the Hurricane Ike significantly extended the polluted area.

Fast reconstruction of computerized tomography images based on the cross-entropy method

Computerized tomography (CT) has been applied to multi-phase flow measurement in recent years. Image reconstruction of CT often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive, especially for the case of on-line flow regime identification. In this paper, a minimum cross-entropy (MCE) reconstruction based on wavelet multi-resolution processing, i.e., an MRMCE method, is proposed for fast reconstruction of CT images. Each row of the system’s matrix is transformed by 1-D wavelet decomposition. A regularized MCE solution is obtained using the simultaneous multiplicative algebraic reconstruction technique (SMART) at a coarse resolution level, where important information of the reconstructed image is contained. Then the solution in the finest resolution is obtained by inverse fast wavelet transformation (IFWT). Both computer simulation and experimental work were carried out for oil–gas two-phase flow regimes. Results obtained indicate that the MRMCE method improves the resolution of the reconstructed images and dramatically reduces the computation time compared with the traditional linear back-projection (LBP), MCE and algebraic reconstruction technique (ART) methods. Furthermore, the new method can also be used to accurately estimate the local time-averaged void fraction of dynamic two-phase flow. It is suitable for on-line multi-phase flow measurement.

Frame permutation quantization

Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering of the frame expansion coefficients. Compared to ordinary permutation source coding, FPQ produces a greater number of possible quantization rates and a higher maximum rate. Various representations for the partitions induced by FPQ are presented, and reconstruction algorithms based on linear programming, quadratic programming, and recursive orthogonal projection are derived. Implementations of the linear and quadratic programming algorithms for uniform and Gaussian sources show performance improvements over entropy-constrained scalar quantization for certain combinations of vector dimension and coding rate. Monte Carlo evaluation of the recursive algorithm shows that mean-squared error (MSE) decays as M − 4 for an M-element frame, which is consistent with previous results on optimal decay of MSE. Reconstruction using the canonical dual frame is also studied, and several results relate properties of the analysis frame to whether linear reconstruction techniques provide consistent reconstructions.

Optical imaging using spatially resolved reconstruction of steady-state luminescence

Abstract Objective A cancer diagnostics method is proposed using the 3D reconstruction of luminescence-based optical imaging data. Material and methods The diffusion equation solution for a cube was used to tackle the forward problem. The forward solution for two-layered media is also applied in the reconstruction method. The inverse problem was solved using a linear reconstruction technique based on the approximation that the light source needing reconstruction can be decomposed into a weighted sum of unit light sources positioned at each node in the search volume. The calculation for the light propagation in the forward problem was done using values cited in literature for the optical properties of the involved tissue. Results The system was tested with numerical simulations that assumed correct as well as erroneous values of the optical coefficients for canine prostate at 810 nm. The quantitative accuracy of reconstructed sources diminished from 100% to approximately 50% with an increase from 0 to 50% in the error for the values of the absorption coefficient, and from 0 to 20% in the error for the values of the reduced scattering coefficient, respectively. Conclusion The absolute determination of the tumor locations is dependent on the information gathered by the recorded data by the detectors monitoring the light propagation through the tissue under investigation. For a determined or an over-determined system, the locations have been extracted accurately, and partially determined for an under-determined system.