Fast Inversion Method Research Articles

Fingerprint authentication based on deep convolutional descent inversion tomography

Fingerprint authentication is widely used in various areas. While existing methods effectively extract and match fingerprint features, they encounter difficulties in detecting wet fingers and identifying false minutiae. In this paper, a fast fingerprint inversion and authentication method based on Lamb waves is developed by integrating deep learning and multi-scale fusion. This method speeds up the inversion performance through deep fast inversion tomography (DeepFIT) and uses Mask R-CNN to improve authentication accuracy. DeepFIT utilizes fully connected and convolutional operations to approach the descent gradient, enhancing the efficiency of ultrasonic array reconstruction. This suppresses artifacts and accelerates sub-millimeter-level fingerprint minutia inversion. By identifying the overall morphological relationships of various minutia in fingerprints, meaningful minutia representing individual identities are extracted by the Mask R-CNN method. It segments and matches multi-scale fingerprint features, improving the reliability of authentication results. Results indicate that the proposed method has high accuracy, robustness, and speed, optimizing the entire fingerprint authentication process.

A fast inversion method of parameters for contact binaries based on differential evolution

With the development of modern astronomical observation techniques and contact binary research, a large number of light curves of contact binaries have been published, and it has become a challenge to quickly derive the basic physical parameters of contact binaries from their light curves. This article presents a neural network (NN) based on the differential evolution intelligent optimization algorithm to infer the fundamental physical parameters of contact binaries from their light curve. Based on a large dataset of light curves and parameter data generated by Phoebe, a NN mapping model is established, while Differential Evolution (DE) and Markov Chain Monte Carlo (MCMC) algorithms are used to find reasonable parameter combinations, respectively. The experiments show that the parameter inversion speed of the DE algorithm is approximately 50% faster than that of the MCMC algorithm, while guaranteeing a parameter accuracy at least consistent with the those of MCMC algorithm.

Multiscale Inversion of Leaf Area Index in Citrus Tree by Merging UAV LiDAR with Multispectral Remote Sensing Data

The LAI (leaf area index) is an important parameter describing the canopy structure of citrus trees and characterizing plant photosynthesis, as well as providing an important basis for selecting parameters for orchard plant protection operations. By fusing LiDAR data with multispectral data, it can make up for the lack of rich spatial features of multispectral data, thus obtaining higher LAI inversion accuracy. This study proposed a multiscale LAI inversion method for citrus orchard based on the fusion of point cloud data and multispectral data. By comparing various machine learning algorithms, the mapping relationship between the characteristic parameters in multispectral data and point cloud data and citrus LAI was established, and we established the inversion model based on this, by removing redundant features through redundancy analysis. The experiment results showed that the BP neural network performs the best at both the community scale and the individual scale. After removing redundant features, the R2, RMSE, and MAE of the BP neural network at the community scale and individual scale were 0.896, 0.112, 0.086, and 0.794, 0.408, 0.328, respectively. By adding the three-dimensional gap fraction feature to the two-dimensional vegetation index features, the R2 at community scale and individual scale increased by 4.43% and 7.29%, respectively. The conclusion of this study suggests that the fusion of point cloud and multispectral data exhibits superior accuracy in multiscale citrus LAI inversion compared to relying solely on a single data source. This study proposes a fast and efficient multiscale LAI inversion method for citrus, which provides a new idea for the orchard precise management and the precision of plant protection operation.

Fast and efficient inversion methods for crack sizing using Bz magnetic signature

AbstractFast estimation is a critical feature of the proposed modeling approach as a “forward” fast solver that has a key role in solving the “inverse” problem involved in crack sizing, especially for real‐time applications. To this end, two different inversion methods have been proposed to estimate the crack depth. The first one uses an interpolation model of the 3D direct model simulation data. The second approach is based on artificial neural networks (ANN). In this article, the rotating uniform eddy current (RUEC) probe is used to detect the normal magnetic component Bz which is defined as the characteristic signal for reconstructing the crack length and depth concurrently. Using the first approach, The Bz characteristic 3D surface is presented, and this can be modeled by a fitted polynomial interpolation equation. Thus, the crack depth can be inverted using this equation referring to the experimental or simulated Bz signal and the crack length. The ANN is outlined to determine the crack depth based on the simulated Bz signature. The move from the first inversion method to the second was flexible and useful, in which the interpolation model is used as a defect signal generator for fast building of a large and efficient database for ANN training. Both of the proposed methods proved the objectivity and accuracy of the inversion results and offered more robust engineering support for automated NDT, reducing production time and increasing productivity.

Fast and direct inversion methods for the multivariate nonequispaced fast Fourier transform

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various applications such as MRI and solution of PDEs are interested in the inverse problem, i.e., computing Fourier coefficients from given nonequispaced data. In this article, we survey different kinds of approaches to tackle this problem. In contrast to iterative procedures, where multiple iteration steps are needed for computing a solution, we focus especially on so-called direct inversion methods. We review density compensation techniques and introduce a new scheme that leads to an exact reconstruction for trigonometric polynomials. In addition, we consider a matrix optimization approach using Frobenius norm minimization to obtain an inverse NFFT.

Fast inversion method for seepage parameters of core earth-rock dam based on LHS-SSA-MKELM fusion surrogate model

The inversion of seepage parameters is an important research topic in the safety evaluation of earth-rock dams. Core earth-rock dam is a commonly used structural type in earth-rock dams. Most of the existing inversion methods focus on concrete dams, and few of them are aimed at earth-rock dams. These methods have the problems of slow inversion speed or low accuracy. Aiming at the above problems, this paper proposes a novel fast inversion method for the seepage parameters of core earth-rock dams based on the LHS-SSA-MKELM fusion surrogate model. The proposed fusion inversion model optimizes the selection of combination models based on the surrogate model framework, making it more suitable for the inversion calculation of seepage parameters in earth-rock dams. First, based on the seepage theory of earth-rock dams, the finite element numerical simulation model of core earth-rock dam seepage is constructed. The Latin Hypercube Sampling (LHS) method is used to obtain the parameter sample dataset according to the range of the seepage parameters, and the sample dataset is substituted into the finite element model to obtain the corresponding theoretical seepage pressure of different datasets. Then, the Mixed Kernel Extreme Learning Machine (MKELM) is used to establish the mapping relationship between seepage parameters and the theoretical seepage pressure. The MKELM parameters were optimized by using the Sparrow Search Algorithm (SSA) to further improve the accuracy of the surrogate model. Finally, taking the minimum error between the theoretical value and the measured value of the surrogate model as the objective function, the SSA algorithm is used to derive the optimal inversion value of seepage parameters. The results of engineering examples show that the mean absolute percentage error between the measured value of the core earth-rock dam seepage pressure and the simulated value after inversion is only 4.958%. In addition, the average inversion time of the proposed surrogate model is only 6.6 s, which greatly reduces the time-consuming problem of numerical simulation. The proposed method provides a new way for accurate and fast inversion of seepage parameters of core earth-rock dams after long-term operation.

Papua New Guinea Moho inversion based on XGM 2019e gravity field model

The construction of the high-resolution Moho depth model is significant for studying the characteristics of the complex tectonic movement (seafloor spreading, plate subduction phenomena) in Papua New Guinea. We calculate the region’s Moho relief and lithosphere thinning factor using the XGM 2019e gravity field model and nonlinear fast gravity inversion method under the GEMMA Moho depth model’s constraint considering the influence of lithosphere thermal gravity anomaly. The calculation result shows that the Moho depth is between 6—34 km, forming two large depressions in Woodlark Basin (WB) and Solomon Sea Plate (SSP) with deep scattered islands. In addition, the findings suggest that Significant differences exist in the shape and tectonic movement intensity of the North and South oceanic crust at the WB. Nevertheless, the lithosphere extends evenly in Manus Basin (MB). WB collided with the Solomon Islands at a higher angle than the SSP subducted under Bismarck Sea Plate (BSP); strong earthquakes may frequently occur on both sides and in deeper positions at West New Britain Trench in the future.

Comparison of a fast low spatial resolution inversion method and peaking factors for the detection of anomalous radiation patterns and disruption prediction

The prediction of a disruptive event is a fundamental task for future fusion reactors. On current tokamaks, most remedial actions have the aim of mitigating their effects, but in future machines avoiding such events will be indispensable. As reported in the literature, especially in metallic machines, electron temperature anomalies play a significant role in the destabilisation of MHD modes, leading to disruptions. Plasma radiation has a strong influence on the shape of the electron temperature profile but it is measured by bolometers integrating along viewing cones; therefore tomographic inversion methods are required to obtain local radiation information. Unfortunately, tomographic algorithms are usually slow and not applicable in real-time, implying that they cannot be used for disruption prediction. In this work, we propose a simple, low spatial resolution but fast inversion method that allows calculating the radiation power in the most important regions of the vessel. The method proposed is compared with traditional indicators based on radiation peaking factors. It is shown that, with this fast tomographic algorithm, it is possible to detect and classify anomalous radiation patterns, such as core radiation and MARFEs, and to predict upcoming electron temperature anomalies with much better accuracy and reliability than using simple peaking factors.

Gravity and magnetic fast inversion method with cross-gradient based on function fitting

SUMMARY The underground density and magnetic susceptibility structure obtained by cross-gradient inversion of gravity and magnetic data can provide an important basis for the evaluation of mineral resource potential. The inversion is realized by discretizing the subsurface into a series of cells and calculating the physical properties of each cell. This restricts the application in the inversion of large-area data because of the large memory usage and low computational efficiency owing to the large solution matrix. We proposed a high-efficiency cross-gradient inversion method of gravity and magnetic data based on function fitting, which uses a parametrized function to fit the physical properties of the central points of a number of cells in certain space based on the assumption that the physical property in each cell is uniform in the inversion. Therefore, the calculation of physical properties is replaced by the calculation of function coefficients. The number of cells that can be fitted by a function is more than the number of function coefficients. Thus, the new method requires less memory and can improve computational efficiency. In addition, with the function fitting method, the gradient terms can be directly obtained by the function coefficients instead of using the traditional central difference or multipoint fitting method, which could further improve the computational efficiency. The effectiveness and high computational efficiency of the proposed method were verified by model tests, and the accuracy of the inversion results was not lower than that of the traditional inversion method. We also proved that the proposed method is suitable for uniform hexahedral and unstructured tetrahedral cells. The real application area is located in eastern China and contains skarn-type magnetite deposits, which are characterized by high density and high magnetic susceptibility. The proposed method was used to obtain subsurface high-resolution density and magnetic susceptibility structures. We obtained the distribution range of mineral resources based on the ratio of density to magnetic susceptibility, which provides an important basis for further exploration. The model tests and real data applications show that the proposed method is more suitable for large-scale precise inversion and has better practicability.

A fast inversion method for ocean parameters based on dispersion curves with a single hydrophone

A fast inversion method for ocean parameters based on dispersion curves with a single hydrophone

Dyadic diagonalization of positive definite band matrices and efficient [formula omitted]-spline orthogonalization

A dyadic algorithm for diagonalizing an arbitrary positive definite band matrix, referred to as a band Gramian, is obtained to efficiently orthogonalize the B-splines. The algorithm can be also used as a fast inversion method for a band Gramian characterized by remarkable sparsity of the diagonalizing matrix. There are two versions of the algorithm: the first one is more efficient and is applicable to a Toeplitz band Gramian while the second one is more general, works with any Gramian matrix, but is more computationally intensive. In the context of the B-splines, these two cases result in new symmetric orthogonalization procedures and correspond to equally and arbitrarily spaced knots, respectively. In the algorithm, the sparsity of a band Gramian is utilized to produce a natural dyadic net of orthogonal splines, rather than a sequence of them. Such a net is thus naturally referred to as a splinet. The splinets exploit “near-orthogonalization” of the B-splines and feature locality expressed through a small size of the total support set and computational efficiency that is a result of a small number of inner product evaluations needed for their construction. These and other efficiencies are formally quantified by upper bounds and asymptotic rates with respect to the number of splines in a splinet. An additional assessment is provided through numerical experiments. They suggest that the theoretical bounds are rather conservative and the method is even more efficient than the bounds indicate. The dyadic net-like structures and the locality bear some resemblance to wavelets but in fact, the splinets are fundamentally different because they do not aim at capturing the resolution scales. The orthogonalization method together with efficient spline algebra and calculus has been implemented in R-package Splinets available on CRAN.

Fast inversion method of structural parameters based on PCE surrogate model and Bayesian optimization

Fast inversion method of structural parameters based on PCE surrogate model and Bayesian optimization

Deformation early-warning index for heightened gravity dam during impoundment period

The mechanical parameters of materials in a dam body and dam foundation tend to change when dams are reinforced in aging processes. It is important to use an early-warning index to reflect the safety status of dams, particularly of heightened projects in the impoundment period. Herein, a new method for monitoring the safety status of heightened dams is proposed based on the deformation monitoring data of a dam structure, a statistical model, and finite-element numerical simulation. First, a fast optimization inversion method for estimation of dam mechanical parameters was developed, which used the water pressure component extracted from a statistical model, an improved inversion objective function, and a genetic optimization iterative algorithm. Then, a finite element model of a heightened concrete gravity dam was established, and the deformation behavior of the dam with rising water levels in the impoundment period was simulated. Subsequently, mechanical parameters of aged dam parts were calculated using the fast optimization inversion method with simulated deformation and the water pressure deformation component obtained by the statistical model under the same conditions of water pressure change. Finally, a new early-warning index of dam deformation was constructed by means of the forward-simulated deformation and other components of the statistical model. The early-warning index is useful for forecasting dam deformation under different water levels, especially high water levels.

A fast inversion method of 2D nuclear magnetic resonance based on the novel hybrid algorithm

To make up for the limitations and improve the accuracy of 1D nuclear-magnetic-resonance (NMR) logging in the evaluation of formation fluid properties, 2D NMR logging has become the focus of research. Increasing the sequence and inversion parameters of the 2D NMR can effectively improve the antinoise properties and resolution of the inversion, but at the same time, the reduced inversion speed and increased memory occupied will put forward higher requirements on the computer configuration and add to the cost of calculation, which poses challenges to the application of the traditional 2D NMR inversion algorithms. In view of the above defects, we have developed a new fast 2D NMR inversion LSQR-RSVD hybrid algorithm, and we have used the nonnegative least-squares (LSQR) calculation result as the initial value of the RSVD inversion. Taking oil-water and gas-water models as examples, the 2D NMR inversion effects of ( T2, D), ( T1, T2) are analyzed in detail, and ( T1, D) is also discussed by several groups of echo trains with variable echo interval ( TE) and waiting time ( TW). Compared to the inversion algorithm commonly used, the new hybrid algorithm can improve the inversion speed and significantly reduce the memory occupancy. Its remarkable advantages can further promote the application of 2D and even multidimensional NMR logging in practice.

Thin interbed AVA inversion based on a fast algorithm for reflectivity

Zoeppritz equations form the theoretical basis of most existing amplitude variation with incident angle (AVA) inversion methods. Assuming that only primary reflections exist, that is, the multiples are fully suppressed and the transmission loss and geometric spreading are completely compensated for, Zoeppritz equations can be used to solve for the elastic parameters of strata effectively. However, for thin interbeds, conventional seismic data processing technologies cannot suppress the internal multiples effectively, nor can they compensate for the transmission loss accurately. Therefore, AVA inversion methods based on Zoeppritz equations or their approximations are not applicable to thin interbeds. In this study, we propose a prestack AVA inversion method based on a fast algorithm for reflectivity. The fast reflectivity method can compute the full-wave responses, including the reflection, transmission, mode conversion, and internal multiples, which is beneficial to the seismic inversion of thin interbeds. A further advantage of the fast reflectivity method is that the partial derivatives of the reflection coefficient with respect to the elastic parameters can be expressed as analytical solutions. Based on the Gauss–Newton method, we construct the objective function and model-updating formula considering sparse constraint, where the Jacobian matrix takes the form of an analytical solution, which can significantly accelerate the inversion convergence. We validate our inversion method using numerical examples and field seismic data. The inversion results demonstrate that the fast reflectivity-based inversion method is more effective for thin interbed models in which the wave-propagation effects, such as interval multiples, are difficult to eliminate.

Fast matrix inversion methods based on Chebyshev and Newton iterations for zero forcing precoding in massive MIMO systems

In massive MIMO (mMIMO) systems, large matrix inversion is a challenging problem due to the huge volume of users and antennas. Neumann series (NS) and successive over relaxation (SOR) are two typical methods that solve such a problem in linear precoding. NS expands the inverse of a matrix into a series of matrix vector multiplications, while SOR deals with the same problem as a system of linear equations and iteratively solves it. However, the required complexities for both methods are still high. In this paper, four new joint methods are presented to achieve faster convergence and lower complexity in matrix inversion to determine linear precoding weights for mMIMO systems, where both Chebyshev iteration (ChebI) and Newton iteration (NI) are investigated separately to speed up the convergence of NS and SOR. Firstly, joint Chebyshev and NS method (ChebI-NS) is proposed not only to accelerate the convergence in NS but also to achieve more accurate inversion. Secondly, new SOR-based approximate matrix inversion (SOR-AMI) is proposed to achieve a direct simplified matrix inversion with similar convergence characteristics to the conventional SOR. Finally, two improved SOR-AMI methods, NI-SOR-AMI and ChebI-SOR-AMI, are investigated for further convergence acceleration, where NI and ChebI approaches are combined with the SOR-AMI, respectively. These four proposed inversion methods provide near optimal bit error rate (BER) performance of zero forcing (ZF) case under uncorrelated and correlated mMIMO channel conditions. Simulation results verify that the proposed ChebI-NS has the highest convergence rate compared to the conventional NS with similar complexity. Similarly, ChebI-SOR-AMI and NI-SOR-AMI achieve faster convergence than the conventional SOR method. The order of the proposed methods according to the convergence speed are ChebI-SOR-AMI, NI-SOR-AMI, SOR-AMI, then ChebI-NS, respectively. ChebI-NS has a low convergence because NS has lower convergence than SOR. Although ChebI-SOR-AMI has the fastest convergence rate, NI-SOR-AMI is preferable than ChebI-SOR-AMI due to its lower complexity and close inversion result.

Near-real-time near-surface 3D seismic velocity and uncertainty models by wavefield gradiometry and neural network inversion of ambient seismic noise

With the advent of large and dense seismic arrays, novel, cheap, and fast imaging and inversion methods are needed to exploit the information captured by stations in close proximity to each other and produce results in near real time. We have developed a sequence of fast seismic acquisition for dispersion curve extraction and inversion for 3D seismic models, based on wavefield gradiometry, wave equation inversion, and machine-learning technology. The seismic array method that we use is Helmholtz wave equation inversion using measured wavefield gradients, and the dispersion curve inversions are based on a mixture of density neural networks (NNs). For our approach, we assume that a single surface wave mode dominates the data. We derive a nonlinear relationship among the unknown true seismic wave velocities, the measured seismic wave velocities, the interstation spacing, and the noise level in the signal. First with synthetic and then with the field data, we find that this relationship can be solved for unknown true seismic wave velocities using fixed point iterations. To estimate the noise level in the data, we need to assume that the effect of noise varies weakly with the frequency and we need to be able to calibrate the retrieved average dispersion curves with an alternate method (e.g., frequency wavenumber analysis). The method is otherwise self-contained and produces phase velocity estimates with tens of minutes of noise recordings. We use NNs, specifically a mixture density network, to approximate the nonlinear mapping between dispersion curves and their underlying 1D velocity profiles. The networks turn the retrieved dispersion model into a 3D seismic velocity model in a matter of seconds. This opens the prospect of near-real-time near-surface seismic velocity estimation using dense (and potentially rolling) arrays and only ambient seismic energy.

Bayesian well-test 2D tomography inversion for CO2 plume detection

The inversion of cross-well time-lapse pressure tests is investigated as a monitoring technique for locating CO2 plumes in the subsurface. Fast inversion methods are possible which treat the gas plume as either a constant-pressure or reduced diffusivity region. However, neither constant-pressure nor diffusivity-barrier approaches are adequate for modelling the full behaviour of the plume dynamics, especially the late time pressurisation of small plumes. The saturation dependence of the flow is dominated by the compressibility contrast, which justifies the use of an approximate mixed-phase flow equation with saturation dependence confined to the compressibility terms. This fast proxy flow model enables the construction of efficient inversion methods using either low dimensional object–based representations of the plume, or voxelised models exploiting gradients from nonlinear adjoint theory. It allows the inclusion both of cross-well and single-well responses.The inversion algorithms are then tested on a simplified three-dimensional full-physics simulation model of CO2 injection, and give a 2D image for the most probable plume location. By using subsets of the full well data, it is shown that the inversion algorithms can detect and locate the plume with only three monitoring wells, but even two monitoring wells have utility given prior information. More certain delineation of the plume geometry occurs as the number of wells increases, and it is most clearly inferred when the testing well geometry fully surrounds the plume.

Acceleration of 3D potential field data inversion using a BB iterative algorithm

As the big-data age arrives, the efficiency of three dimensional inversions of potential field data can be paid enough attention by scholars. A new inversion method is considered to deal with the large potential field data with a fast rate of convergence. Hence, in this paper, a fast inversion method is researched. And the gravity data is used as an example of potential field data to test the efficiency of our inversion method. To achieve this aim, the study region will be divided into huge amounts of rectangular prisms with unknown constant physical properties of rock. The traditional smooth inversion method is the main principle, and a new Barzilai-Borwein iterative algorithm is applied to ensure the rapid rate of convergence of the inversion method. To compare the rate of convergence of the BB (Barzilai-Borwein) iterative algorithm, the iterative gradient descent algorithm and the iterative conjugate gradient algorithm are used as the compared algorithms. To test high efficiency of the new fast developed inversion method, the large synthetic gravity data are performed. The contrast analysis results can easily reflect the high efficiency of our new inversion method. The great practical value of our inversion method is expounded by a real gravity data. Therefore, the new inversion method may have a great influence on the potential field data inversion.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the “big data” category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.