Iterative Inversion Method Research Articles

Fourier Bases-Expansion Contraction Integral Equation for Inversion Highly Nonlinear Inverse Scattering Problem

The electromagnetic inverse scattering problems (ISPs) have counted severe multiple scattering effects, especially those for strong scatterers (the ones with high contrasts and/or electrically large dimensions). Iterative inversion methods based on the model of the Lippmann–Schwinger integral equation (LSIE) usually fail to reconstruct such highly nonlinear ISPs. In this article, in virtue of a new recently established contraction integral equation for inversion (CIE-I), we propose a Fourier bases-expansion with CIE-I (FBE-CIE-I) inversion method to handle highly nonlinear ISPs via the contrast source inversion (CSI) scheme. In the FBE-CIE-I, the unknown contrast source is spanned within the Fourier bases, and the multi-round optimization scheme is adopted by choosing the proper number of low-frequency components; not only the model of CIE-I can be stabilized well but also the computational cost can be further reduced compared with the traditional CSI. Besides, compared with the previous inversion method based on LSIE, the resolvability and robustness of the FBE-CIE-I could be significantly enhanced in handling highly nonlinear ISPs. Numerical and experimental tests verify the interests and efficiency of the proposed method.

Multiplicatively Regularized Iterative Updated Background Inversion Method for Inverse Scattering Problems

A multiplicatively regularized iterative updated background method (MR-IUBM) based on difference integral equations is proposed to solve the electromagnetic inverse scattering problems (ISPs) involving both inhomogeneous and homogeneous background media. This aims to improve the ability for solving highly nonlinear ISPs with source-typed inversion solver by consistently updating the inhomogeneous background media from the updated unknown scatterers via the use of the Green's function with homogeneous medium. In virtue of MR into the cost function, the stability and the capability of tackling highly nonlinear ISPs can be further greatly improved. Synthetic and experimental results are presented to illustrate the efficiency of this method.

Motions Planning for Virtual Character

The existence of a virtual character in an environment requires its interaction within it. This interaction involves a combination of two skills, which are locomotion and manipulation. Our method treats this type of full-body motion planning problems. Where locomotion and manipulation are planned separately and coordinated with each other. We use a locomotion planner based on motion graph that searches for convenient body position for performing the manipulation motions successfully, and combined with a an iterative inverse kinematic method. The IK method adjusts the upper-body end effectors in real time to new constraints for planning manipulation motions. As a result, our method is able to automatically coordinate whole-body motions for planning virtual character locomotion and manipulation.

Motions Planning for Virtual Character

The existence of a virtual character in an environment requires its interaction within it. This interaction involves a combination of two skills, which are locomotion and manipulation. Our method treats this type of full-body motion planning problems. Where locomotion and manipulation are planned separately and coordinated with each other. We use a locomotion planner based on motion graph that searches for convenient body position for performing the manipulation motions successfully, and combined with a an iterative inverse kinematic method. The IK method adjusts the upper-body end effectors in real time to new constraints for planning manipulation motions. As a result, our method is able to automatically coordinate whole-body motions for planning virtual character locomotion and manipulation.

A Low Complexity Near-Optimal Iterative Linear Detector for Massive MIMO in Realistic Radio Channels of 5G Communication Systems.

Massive multiple-input multiple-output (M-MIMO) is a substantial pillar in fifth generation (5G) mobile communication systems. Although the maximum likelihood (ML) detector attains the optimum performance, it has an exponential complexity. Linear detectors are one of the substitutions and they are comparatively simple to implement. Unfortunately, they sustain a considerable performance loss in high loaded systems. They also include a matrix inversion which is not hardware-friendly. In addition, if the channel matrix is singular or nearly singular, the system will be classified as an ill-conditioned and hence, the signal cannot be equalized. To defeat the inherent noise enhancement, iterative matrix inversion methods are used in the detectors’ design where approximate matrix inversion is replacing the exact computation. In this paper, we study a linear detector based on iterative matrix inversion methods in realistic radio channels called QUAsi Deterministic RadIo channel GenerAtor (QuaDRiGa) package. Numerical results illustrate that the conjugate-gradient (CG) method is numerically robust and obtains the best performance with lowest number of multiplications. In the QuaDRiGA environment, iterative methods crave large to obtain a pleasurable performance. This paper also shows that when the ratio between the user antennas and base station (BS) antennas () is close to 1, iterative matrix inversion methods are not attaining a good detector’s performance.

Model-Based Reconstruction of Large Three-Dimensional Optoacoustic Datasets.

Iterative model-based algorithms are known to enable more accurate and quantitative optoacoustic (photoacoustic) tomographic reconstructions than standard back-projection methods. However, three-dimensional (3D) model-based inversion is often hampered by high computational complexity and memory overhead. Parallel implementations on a graphics processing unit (GPU) have been shown to efficiently reduce the memory requirements by on-the-fly calculation of the actions of the optoacoustic model matrix, but the high complexity still makes these approaches impractical for large 3D optoacoustic datasets. Herein, we show that the computational complexity of 3D model-based iterative inversion can be significantly reduced by splitting the model matrix into two parts: one maximally sparse matrix containing only one entry per voxel-transducer pair and a second matrix corresponding to cyclic convolution. We further suggest reconstructing the images by multiplying the transpose of the model matrix calculated in this manner with the acquired signals, which is equivalent to using a very large regularization parameter in the iterative inversion method. The performance of these two approaches is compared to that of standard back-projection and a recently introduced GPU-based model-based method using datasets from in vivo experiments. The reconstruction time was accelerated by approximately an order of magnitude with the new iterative method, while multiplication with the transpose of the matrix is shown to be as fast as standard back-projection.

Crustal nature and lithospheric structure of the Okinawa Trough

The Okinawa Trough (OT) is a back‐arc basin located in the eastern edge of the Eurasian Plate. The stage of back‐arc spreading and the exact crustal thickness of the OT are still controversial. To determine the crustal nature and lithospheric structure of the OT, the Moho discontinuity depth of the OT is calculated through the Parker–Oldenburg iterative inversion method based on the Bouguer gravity anomaly data in this article. The result shows that the crustal thickness of the OT is 15–27 km, thinner than those of the typical continental crust, and thicker than those of the normal oceanic crust. In this study, the formation and evolution of marginal basins or back‐arc basins is divided into four stages based on the crustal thickness of the basin. By comparing crustal thickness and heat flow of typical marginal basins located in global passive continental margins and continental rift, it can be inferred that the OT is at a stage later than continental drift. We suggest that the southern and middle OT are at the early stage of back‐arc spreading, while the northern OT is still at the ocean–continent transitional stage. There may have been initial oceanic crust developed at the spreading center in the southern OT. The tomographic images of the OT show that there is low‐velocity anomalous mantle beneath the OT, providing deep geophysical evidence for back‐arc spreading of the OT.

Risley-prism-based tracking model for fast locating a target using imaging feedback.

Fast imaging tracking technology exhibits attractive application prospects in the emerging fields of target tracking and recognition. Smart and compact tracking model with fast and flexible tracking strategy can play a decisive role in improving system performance. In this paper, an effective imaging tracking model from a target to a rotation Risley prism pair embedded with a camera is derived by the beam vector propagation method. A boresight adjustment strategy using the inverse ray tracing and iterative refinement method is established to accomplish the function of fast locating a target. The influence of system parameters on boresight adjustment accuracy and even the dynamic characteristics of the tracking system are investigated to reveal the coupling mechanisms between prism rotation and imaging feedback. The root-mean-square tracking error is below 4.5 pixels by just once adjustment in the static target experiment, while the error in the dynamic experiment is below 8.5 pixels for a target moving at the speed of 50 mm/s, which validates the feasibility of the proposed method for fast imaging tracking applications.

Heat partition in edge trimming of fiber reinforced polymer composites

Thermal loading of fiber reinforced composites during traditional machining is inevitable. This is due to the fact that most of the mechanical energy utilized in material removal is converted into heat, which is subsequently dissipated into the workpiece and the cutter, and is carried away by the chips. Heat conduction into the workpiece during machining might cause thermal damage due to matrix softening and decomposition if the generated temperatures exceeded the glass transition temperature of the epoxy resin. In this work, the amount of heat flux applied to the machined edge and the temperature distribution in multidirectional CFRP and GFRP composite laminates was determined using an iterative inverse heat conduction method. The transient heat conduction problems in the laminate and cutter were simulated independently using the finite element method and the amount of heat flux applied to each was determined. It was also found that the heat flux conducted to the workpiece represented only a small fraction of the total heat and is more influenced by the feed speed than the spindle speed. The temperature of the machined surface was estimated and correlations with the resulting machined surface texture were made.

Characterization of a vertical crack using Laser Spot Thermography

ABSTRACT This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures, emerging on the accessible surface of a slab, by means of Active Thermography. In real life, this surface is heated with a laser and its temperature is measured for a time interval by means of an infrared camera. A fundamental step in iterative inversion methods is the numerical solution of the underlying direct mathematical model. Usually, this step requires specific techniques in order to limit an abnormal use of memory resources and computing time due to excessively fine meshes necessary to follow a very thin fracture in the domain. Our contribution to this problem consists in decomposing the temperature of the damaged specimen as a sum of a term (with known analytical form) due to an infinite virtual fracture and the solution of an initial boundary value problem for the heat equation on one side of the fracture (i.e. on a rectangular domain). The depth of the fracture is a variable parameter in the boundary conditions that must be estimated from additional data (usually, measurements of the surface temperature). We apply our method to the detection of simulated cracks in concrete and steel specimens.

The revisited total least squares problems with linear equality constraint

The total least squares problem with linear equality constraint is proved to be approximated by an unconstrained total least squares problem with a large weight on the constraint. A criterion for choosing the weighting factor is given, and a QR-based inverse (QR-INV) iteration method is presented. Numerical results show that the QR-INV method is more efficient than the standard QR-SVD procedure and Schaffrin's inverse iteration method, especially for large and sparse matrices.

A Comparative Study of Direct and Iterative Inversion Approaches to Determine the Spatial Shear Modulus Distribution of Elastic Solids

This paper presents a comparative study of two typical inverse algorithms, i.e., direct and iterative inversion methods, to reconstruct the shear modulus distribution of linearly elastic solids. Both approaches are based on the finite element framework and compared utilizing both the simulated and experimental data. The reconstruction results demonstrate that both approaches are capable of identifying the nonhomogeneous shear modulus distribution of solids well. It can also be found that the direct inversion method is much faster than the iterative inversion method, whereas the iterative inversion method is capable of yielding better shear modulus ratio between the stiff inclusion and the soft background even with very high noise levels. Afterwards, a thorough comparison on the advantages and disadvantages of these two approaches has been performed. This comparative study provides useful information on the selection of the proper inverse scheme in estimating nonhomogeneous elastic property distribution of soft solids nondestructively.

Quick and Highly Efficient Modal Analysis Method Based on the Reanalysis Technique for Large Complex Structure and Topology Optimization

Modal analysis is widely used to investigate the dynamic characteristics of large and complex structures. For finite element models, iterative solvers are needed to precisely calculate eigenpairs or frequency and vibration mode. However, in cases such as large-scale analysis or reanalysis studies, or optimization design of a huge structure, computational cost may become too time consuming. This paper focuses on the quick structural modal analysis based on the reanalysis technique for large complex structures. Based on the stiffness and mass matrix of the analytical structures, a high precision and efficiency eigensolution is generated by the proposed modal analysis method (the Pseudo Random Independent and Coupling Inverse Iteration (PRICII) method), which combines the pseudo random number initialization, ICII (Independent and Coupling Inverse Iteration) strategy with the double Rayleigh–Ritz analysis. By comparing with the Subspace iteration method, Lanczos method, etc. the large-scale numerical examples show that the actual computational savings of the proposed method are usually higher than 75% with sufficient precision. Also, its applications in topology optimization are greatly effective.

Weighted iterative inversion method for T2 spectrum in nuclear magnetic resonance

In traditional nuclear magnetic resonance T2 inversion methods, the components with long T2 absorb the components with short T2, especially for low magnetic field intensity. As a result, the true distribution of all components often cannot be reflected by their solutions, and thus obtaining short T2 components is an important T2 inversion problem. Herein, a weighted iterative inversion method for T2 spectrum in nuclear magnetic resonance is proposed to solve this problem. The weight-based method is applied to ensure that the short T2 components are not eliminated. The weight scheme is determined by two parameters: the number of weights and maximum weight. The number of weights is determined by the rate of decay, and the maximum weight is mainly determined by three parameters: signal-noise ratio, curvature, and slope of collected signal. To avoid the mutations of results caused by weights, the iteration process was adopted to obtain the optimal solution. The proposed method provides good results, and it was verified to be robust and accurate though simulations and experiments.

Applying Iterative Method to Solving High-Order Terms of Seafloor Topography

We introduce an iterative inversion method to address the problems in high-order seafloor topography inversion using gravity data (gravity anomaly and vertical gravity gradient anomaly), such as the difficulty in computing the equation and the uniqueness of the calculation results. A part of the South China Sea is selected as the experimental area. Considering the coherence and admittance function of gravity topography and vertical gravity gradient topography, the inversion band of the gravity anomaly and vertical gravity gradient anomaly in the study area is 30 km–120 km. Seafloor topography models of different orders are constructed using an iterative method, and the performance of each seafloor topography model is analyzed against ETOPO1 and other seafloor topography models. The experimental results show that as the inversion order increases, the clarity and richness of seafloor topographic expression continuously improve. However, the accuracy of seafloor topography inversion does not improve significantly when the inversion order exceeds a certain value, which is related to the contribution of high-order seafloor topography to gravity information. The results show that the accuracy of BGT4 (inversion model constructed by the gravity anomaly) is slightly poorer than that of BVGGT4 (inversion model constructed by the vertical gravity gradient anomaly) in areas with complex topography, such as multi-seamounts and trenches, and the results are generally better in areas with flat seafloor topography.

The impact of a priori elastic models into iterative geostatistical seismic inversion

In reservoir modelling and characterization, the integration of geological information within seismic inversion is critical to efficiently obtain accurate inverted models. The existing knowledge about the subsurface geology should be gathered and used as conditioning data to generate robust a priori models. Usually, these models explain the expected background trend of the subsurface property of interest. One of the main differences between deterministic and iterative geostatistical seismic inversion methods is how the a priori knowledge about the spatial continuity pattern of the subsurface elastic property to be inferred, is used as constraint for the inversion. Deterministic approaches use explicit a priori models, often low-frequency models, to represent the geological background of the inverted properties. On the other hand, iterative global geostatistical seismic inversion methods do not include explicitly a priori models, since the spatial continuity pattern of the elastic property to be inverted is described exclusively by a variogram model. This work explores the impact of using explicit a priori models when integrated into iterative geostatistical seismic inversion methods. Three a priori models were built with different techniques and incorporated into the inversion process using two distinct methodologies: the first directly constrains the generation of elastic models, using stochastic sequential simulation with simple kriging with locally varying means; alternatively, these a priori models are also incorporated as part of a multi-objective function, accounting for both data and model deviations. All scenarios are applied to a synthetic case study, and those with the best results are then applied to a three-dimensional real dataset. The results of this work illustrate the drawbacks and advantages of using explicit a priori models in iterative geostatistical seismic inversion, highlighting the impact on the reproduction of channels under complex and heterogeneous siliciclastic geological environments and the need of reliable a priori models for accurate predictions about the subsurface.

Determination of complex dielectric function of CH3NH3PbBr3 perovskite cubic colloidal quantum dots by modified iterative matrix inversion method.

Recent advances in lead halide perovskite quantum dots appeal with their potential in various optoelectronic devices such as photovoltaics, photodetectors, light-emitting diodes (LEDs) and lasers. However, lack of information on the intrinsic optical properties of lead halide perovskite quantum dots (QDs) lags the progress in device performances and further development in various applications. In this letter, the complex dielectric function of CH3NH3PbBr3 perovskite cubic colloidal QDs was determined from the UV-Vis absorption by using a modified iterative matrix inversion (IMI) method. The modified IMI method takes into account the dilute solution with cubic inclusions, while the conventional method only considers spherical or elliptical inclusions by Maxwell-Garnett (MG) effective medium theory. In addition, singly subtractive Kramer Kronig (SSKK) relations have also been considered to compensate for possible errors arising from the finite wavelength range of the experimental absorption data.

Plasmonic colours predicted by deep learning

Picosecond laser pulses have been used as a surface colouring technique for noble metals, where the colours result from plasmonic resonances in the metallic nanoparticles created and redeposited on the surface by ablation and deposition processes. This technology provides two datasets which we use to train artificial neural networks, data from the experiment itself (laser parameters vs. colours) and data from the corresponding numerical simulations (geometric parameters vs. colours). We apply deep learning to predict the colour in both cases. We also propose a method for the solution of the inverse problem – wherein the geometric parameters and the laser parameters are predicted from colour – using an iterative multivariable inverse design method.

Coupling calculation and analysis of three‐dimensional temperature and fluid field for high‐power high‐speed permanent magnet machine

In order to accurately estimate the temperature rise for high-power high-speed permanent magnet machines (HSPMMs), a novel temperature calculation method considering the non-linear variation of material properties with temperature is proposed based on multi-physics co-simulation analysis. According to the theory of computational fluid dynamics and heat transfer, the computation model of fluid–solid–heat coupling heat transfer is established, and the coupled field is calculated using finite volume method with fundamental assumptions and corresponding boundary conditions. With the influences from temperature gradient and water flow rate considered, the heat transfer coefficients of water pipe surfaces are obtained by the application of the inverse iteration method. Thus, HSPMM temperature and fluid field can be simulated numerically by the finite volume methods, while the spatial temperature distributions for the machine main components are analysed in this study. The 1.12 MW, 18,000 rpm HSPMM is prototyped with experiments conducted on it, while the test data are then compared with the calculated results, which validate the correctness of the solution method of the coupled field.

An inverse method for the abrasive jet micro-machining of high aspect ratio channels of desired topography – Part I, theory

Control of the cross-sectional shape of micro-channels may be of interest in micro-heat-sinks, microfluidic particle sorting, and micro-machine lubrication applications. It has been previously shown that inverse methods can be used to determine the abrasive jet micromachining (AJM) traverse speed and path required to sculpt desired micro-channel topographies, as long as the aspect ratios (AR, ratio of depth to width) are low (<0.06), such that the channel sidewall slopes are negligible. However, for many applications, higher AR channels with steep sidewalls are required. This paper introduces an iterative inverse method which allows prediction of the machining procedure required to sculpt higher (AR up to 1) micro-channels of prescribed cross-sectional shape using mask-less AJM. The method is developed for AJM in both ductile and brittle erosive systems, its robustness and limitations are discussed, and the iterative methodology is compared to the General Reduced Gradient optimization technique. Part II of the paper will experimentally verify the procedure for a wide variety of desired topographies machined in borosilicate glass and Poly(methyl methacrylate) (PMMA).