Electromagnetic Inverse Problem Research Articles

Semantic regularization of electromagnetic inverse problems

Solving ill-posed inverse problems typically requires regularization based on prior knowledge. To date, only prior knowledge that is formulated mathematically (e.g., sparsity of the unknown) or implicitly learned from quantitative data can be used for regularization. Thereby, semantically formulated prior knowledge derived from human reasoning and recognition is excluded. Here, we introduce and demonstrate the concept of semantic regularization based on a pre-trained large language model to overcome this vexing limitation. We study the approach, first, numerically in a prototypical 2D inverse scattering problem, and, second, experimentally in 3D and 4D compressive microwave imaging problems based on programmable metasurfaces. We highlight that semantic regularization enables new forms of highly-sought privacy protection for applications like smart homes, touchless human-machine interaction and security screening: selected subjects in the scene can be concealed, or their actions and postures can be altered in the reconstruction by manipulating the semantic prior with suitable language-based control commands.

Characterizing Lossy Dielectric Materials in Shock Physics by Millimeter-Wave Interferometry Using One-Dimensional Convolutional Neural Networks and Nonlinear Optimization

When a dielectric material undergoes mechanical impact, it generates a shock wave, causing changes in its refractive index. Recent demonstrations have proven that the modified refractive index can be determined remotely using a millimeter-wave interferometer. However, these demonstrations are based on the resolution of an inverse electromagnetic problem, which assumes that the losses in the material are negligible. This restrictive assumption is overcome in this article, in which a new approach is proposed to solve the inverse electromagnetic problem in lossy and shocked dielectric materials. Our methodology combines a one-dimensional convolutional neural network architecture, namely Inverse problem of Lossless or Lossy Shocked Wavefront Network (ILSW-Net), with a nonlinear optimization technique based on the Nelder–Mead algorithm to estimate losses within dielectric materials under a mechanical impact. Experimental results for both simulated and real signals show that our method can successfully predict the velocities and the refractive index while accurately estimating the shock wavefront.

Reciprocal action of natural bianisotropy and artificial chirality on electromagnetic propagation in medium

Background. The present article investigates the reciprocal action of specific medium effects on electromagnetic waves propagation. The object of study is a moving dielectric, which at rest already demonstrate bianisotropic properties, i. e., it is a synthetic material, e. g., chiral media with Ω-particles. Bianisotropic material equations are the most general for describing the effects of electromagnetic waves interaction with complex medium. Studying and analyzing them is proving to be a notable scientific problem. Natural bianisotropy is a property of simple media under special conditions (state of motion, internal currents and diffusion processes), whereas artificial bianisotropy is an inherent property of the synthetic material itself (composite material, material with different metaparticles). Aim. The main goal of the work is to generalize the already available data. On it basis, then, obtain analytical expressions, which can be effectively used for the experiments designing, creating new computational techniques for solving direct and inverse electromagnetic diffraction problems. Methods. In this paper, analytical methods are applied to obtain the resulting close-form expressions. Results. Three classes of effects have been identified that have a significant reciprocal effect on each other: gyrotropy, spatial dispersion, and temporal dispersion. In this article it was shown that the gyrotropy of the medium has not only a simple additive effect, but under some, specific conditions, can be related to the system emergence. Conclusion. The reciprocal action of the spatial dispersion of the moving chiral medium, generally has different scales in range. Temporal dispersion was investigated, which does not have a simple additive property, because even an isotropic medium acquires fundamentally new material properties of bianisotropy when it moves.

Visibility, invisibility and unique recovery of inverse electromagnetic problems with conical singularities

Visibility, invisibility and unique recovery of inverse electromagnetic problems with conical singularities

Uniqueness Results for Some Inverse Electromagnetic Scattering Problems with Phaseless Far-Field Data

Consider three electromagnetic scattering models, namely, electromagnetic scattering by an elastic body, by a chiral medium, and by a cylinder at oblique incidence. We are concerned with the corresponding inverse problems of determining the locations and shapes of the scatterers from phaseless far-field patterns. There are certain essential differences from the usual inverse electromagnetic scattering problems, and some fundamental conclusions need to be proved. First, we show that the phaseless far-field data are invariant under the translation of the scatterers and prove the reciprocity relations of the scattering data. Then, we justify the unique determination of the scatterers by utilizing the reference ball approach and the superpositions of a fixed point source and plane waves as the incident fields. The proofs are based on the reciprocity relations, Green’s formulas, and the analyses of the wave fields in the reference ball.

An information theoretic Bayesian uncertainty analysis of AEM systems over Menindee Lake, Australia

SUMMARY Long-range, active-source airborne electromagnetic (AEM) systems for near-surface conductivity imaging fall into two categories: helicopter (rotary-wing) borne or fixed-wing aircraft borne. A multitude of factors such as flying height, transmitter loop area and current, source waveforms, aerodynamic stability and data stacking times contribute to the geological resolvability of the subsurface. A comprehensive comparison of the relative merits of each system considering all such factors is difficult, but test flights over well-constrained subsurface geology with downhole induction logs are extremely useful for resolution studies. However, given the non-linear nature of the electromagnetic inverse problem, handling transmitter–receiver geometries in fixed-wing aircraft is especially challenging. As a consequence of this non-linearity, inspecting the closeness of downhole conductivities to deterministic inversion results is not sufficient for studying resolvability. A more comprehensive picture is provided by examining the variation in probability mass of the depth-wise Bayesian posterior conductivity distributions for each kind of AEM system within an information theoretic framework. For this purpose, probabilistic inversions of data must be carried out. Each acquiring system should fly over the same geology, survey noise levels must be measured and the same prior probabilities on conductivity must be used. With both synthetic models as well as real data from over the Menindee calibration range in New South Wales, Australia, we shed new light on the matter of AEM inverse model uncertainty. We do this using two information theoretic attributes derived from different Kullback–Leibler divergences—Bayesian information gain, and a strictly proper scoring rule, to assess posterior probabilities estimated by a novel Bayesian inversion scheme. The inversion marginalizes fixed-wing geometry attributes as generic nuisance parameters during Markov chain sampling. This is the first time-domain AEM study we know of, that compares nuisance marginalized subsurface posterior conductivities from a fixed-wing system, with rotary-wing derived posterior conductivities. We also compare field results with induction log data where available. Finally, we estimate the information gain in each case via a covariate shift adaptation technique that has not been used before in geophysical work. Our findings have useful implications in AEM system selection, as well as in the design of better deterministic AEM inversion algorithms.

Shock Properties Characterization of Dielectric Materials Using Millimeter-Wave Interferometry and Convolutional Neural Networks.

In this paper, a neural network approach is applied for solving an electromagnetic inverse problem involving solid dielectric materials subjected to shock impacts and interrogated by a millimeter-wave interferometer. Under mechanical impact, a shock wave is generated in the material and modifies the refractive index. It was recently demonstrated that the shock wavefront velocity and the particle velocity as well as the modified index in a shocked material can be remotely derived from measuring two characteristic Doppler frequencies in the waveform delivered by a millimeter-wave interferometer. We show here that a more accurate estimation of the shock wavefront and particle velocities can be obtained from training an appropriate convolutional neural network, especially in the important case of short-duration waveforms of few microseconds.

Learning-Based Approaches to Current Identification from Magnetic Sensors.

Direct measurement of electric currents can be prevented by poor accessibility or prohibitive technical conditions. In such cases, magnetic sensors can be used to measure the field in regions adjacent to the sources, and the measured data then can be used to estimate source currents. Unfortunately, this is classified as an Electromagnetic Inverse Problem (EIP), and data from sensors must be cautiously treated to obtain meaningful current measurements. The usual approach requires using suited regularization schemes. On the other hand, behavioral approaches are recently spreading for this class of problems. The reconstructed model is not obliged to follow the physics equations, and this implies approximations which must be accurately controlled, especially if aiming to reconstruct an inverse model from examples. In this paper, a systematic study of the role of different learning parameters (or rules) on the (re-)construction of an EIP model is proposed, in comparison with more assessed regularization techniques. Attention is particularly devoted to linear EIPs, and in this class, a benchmark problem is used to illustrate in practice the results. It is shown that, by applying classical regularization methods and analogous correcting actions in behavioral models, similar results can be obtained. Both classical methodologies and neural approaches are described and compared in the paper.

Solving Electromagnetic Inverse Scattering Problems in Inhomogeneous Media by Deep Convolutional Encoder–Decoder Structure

This communication proposes a novel deep learning (DL) approach to solve electromagnetic inverse scattering (EMIS) problems in inhomogeneous media. The conventional approaches for solving inhomogeneous EMIS problems generally have to consider inhomogeneous Green’s functions or conduct approximation operations to media, which inevitably introduces various challenges, including complex mathematical derivation, high computation cost, unavoidable nonlinearity, and even strong ill-posedness. To avoid these challenges, we propose a DL approach based on the complex-valued deep convolutional neural networks (DConvNets), which comprise the deep convolutional encoder–decoder (DCED) structure. Its training data are collected based on the simple synthetic dataset. While the scattered fields received in the measurement domain are utilized as the input for the encoder to extract feature fragments, the final output for the counterpart decoder is the contrasts (permittivities) of dielectric scatterers in the target domain. In this way, unlike the conventional methods, the unknown domain between the target domain and measurement domain never has to be considered to compute inhomogeneous Green’s functions. Consequently, the inhomogeneous EMIS problems could be solved with higher accuracy even for extremely high-contrast targets. Numerical examples illustrate the feasibility of the proposed DL approach. It acts as a new candidate for solving EMIS problems in inhomogeneous media.

FUNCTIONAL-ANALYTICAL RECONSTRUCTION OF HIGH CONTRAST INHOMOGENEITIES

In practice of acoustic tomography, for example, in medical applications and ocean tomography, the relative deviation of sound speed from its background value usually does not exceed 10-30%. At the same time, in electromagnetic applications, the equivalent contrasts can be noticeably higher than 60%. Since the inverse electromagnetic problem can be re- duced in some approximation to Helmholtz equation, a formal comparison of reconstruction results obtained for different "acoustic" contrast and corresponding "dielectric" contrast is possible. In this work examples of such reconstructions are presented, which were obtained by using the functional-analytical algorithm described in works of R.G. Novikov. Previously, the advantages of this algorithm for solving practical problems of acoustic tomography were demonstrated. Results obtained in the present work show that functional-analytical algo- rithm can also be applied to reconstructing inhomogeneities with high "dielectric" contrast. Moreover, the functional algorithm also perfectly reconstructs very small "dielectric" contrast, recovering of which can be difficult for other approaches due to weak backscattering.

Solving Electromagnetic Inverse Problem Using Adaptive Gradient Descent Algorithm

The nonlinear conjugate gradient (NLCG) algorithm is one of the popular linearized methods used to solve the frequency-domain electromagnetic (EM) geophysical inverse problem. During NLCG iterations, the model gradient guides the searching direction while the line-search algorithm determines the step length of each iteration. Normally, the line search requires solving the corresponding forward problem a few times. Since line search is usually computationally inefficient, we introduce the adaptive gradient descent (AGD) algorithm to accelerate solving the frequency-domain EM inverse problem within the linearized framework. The AGD algorithm is a variant of the classical gradient descent method and has been well-developed and widely used in deep learning. Rather than the time-consuming line search, its core idea is to algebraically manipulate the cumulative gradients and updates of the model from previous iterations to estimate the model parameter variables at the current iteration. For the inversion of magnetotelluric (MT) data, we here designed and implemented a framework using the AGD algorithm combined with the cool-down scheme to tune the regularization parameter. To improve the convergence performance of the AGD algorithm [specifying to Adam and root-mean-square propagation (RMSProp)], we proposed a tolerance strategy which has been tested numerically. To optimize the global learning rate, we carried out some comparative trials in the proposed inversion framework. The inverted results of synthetic and real-world data showed that both the AGD algorithms (Adam and RMSProp) can recover comparable results and save more than a third of CPU time compared with the NLCG algorithm.

Recovery of impenetrable rough surface profiles via CNN-based deep learning architecture

ABSTRACT In this paper, a convolutional neural network (CNN)-based deep learning (DL) architecture for the solution of an electromagnetic inverse problem related to imaging of the shape of the perfectly electric conducting (PEC) rough surfaces is addressed. The rough surface is illuminated by a plane wave and scattered field data is obtained synthetically through the numerical solution of surface integral equations. An effective CNN-DL architecture is implemented through the modelling of the rough surface variation in terms of convenient spline type base functions. The algorithm is numerically tested with various scenarios including amplitude only data and shown that it is very effective and useful.

Enhanced Supervised Descent Learning Technique for Electromagnetic Inverse Scattering Problems by the Deep Convolutional Neural Networks

This work proposes a novel deep learning (DL) framework to solve the electromagnetic inverse scattering (EMIS) problems. The proposed framework integrates the complex-valued deep convolutional neural network (DConvNet) into the supervised descent method (SDM) to realize both off-line training and on-line “imaging” prediction for EMIS. The offline training consists of two parts: 1) DConvNet training: the training dataset is created, and the proposed DConvNet is trained to realize the EM forward process and 2) SDM training: the trained DConvNet is integrated into the SDM framework, and the average descent directions between the initial prediction and the true label of SDM iterative schemes are learned based on the same dataset in part 1). In the online step, the contrasts (permittivities) reconstruction of scatterers is realized by the SDM iteration process based on learned descent directions, while its forward process is achieved by the trained complex-valued DConvNet. Ultimately, this framework provides a new perspective to integrate the prior information into the EMIS solving process with the maintained accuracy. Unlike the conventional SDM, the novel proposed framework can significantly shorten the computation and realize the real-time imaging. Various numerical examples and discussions are provided to demonstrate the efficiency and accuracy of the proposed novel framework.

A Hybrid Neural Network Electromagnetic Inversion Scheme (HNNEMIS) for Super-Resolution 3-D Microwave Human Brain Imaging

Super-resolution three-dimensional (3-D) electromagnetic (EM) inversion for microwave human brain imaging is a typical high contrast EM inverse problem and requires huge computational costs. This work proposes a hybrid neural network electromagnetic inversion scheme (HNNEMIS) which contains shallow and deep neural networks to alleviate the required huge computational costs and solve this high contrast inverse problem. In the proposed scheme, semi-join back propagation neural network (SJ-BPNN) is employed to nonlinearly map the measured scattered electric field to two output channels, namely the permittivity and conductivity of scatterers, respectively. Such a semi-join strategy decreases the computational burden in training and testing processes. Then, a deep learning technique, termed U-Net, is employed to further enhance the imaging quality of the output from SJ-BPNN. To decrease the training cost and make neural networks fast convergent for human brain inversion, a novel training dataset construction strategy which contains the characteristics of human brain is also proposed. Noise-free and noisy numerical examples demonstrate that HNNEMIS has superior super-resolution inversion capabilities for human brain imaging.

Deep learning as a tool for inverse problems resolution: a case study

PurposeThis study aims to investigate the possible use of a deep neural network (DNN) as an inverse solver.Design/methodology/approachDifferent models based on DNNs are designed and proposed for the resolution of inverse electromagnetic problems either as fast solvers for the direct problem or as straightforward inverse problem solvers, with reference to the TEAM 25 benchmark problem for the sake of exemplification.FindingsUsing DNNs as straightforward inverse problem solvers has relevant advantages in terms of promptness but requires a careful treatment of the underlying problem ill-posedness.Originality/valueThis work is one of the first attempts to exploit DNNs for inverse problem resolution in low-frequency electromagnetism. Results on the TEAM 25 test problem show the potential effectiveness of the approach but also highlight the need for a careful choice of the training data set.

A Julia software package for transdimensional Bayesian inversion of electromagnetic data over horizontally stratified media

A quantitative assessment of model parameter uncertainty is vital for a reliable interpretation of electromagnetic (EM) data due to the nonuniqueness inherent to EM inverse problems. Conventional gradient-based inversion approaches typically produce a single preferred model with limited information about parameter uncertainty. The inverse problems can be alternatively postulated into a sampling-based Bayesian inference framework where the solution is represented by a posterior probability distribution of model parameters, which can provide an effective way to rigorously estimate parameter uncertainty related to the recovered solution. We have implemented a Bayesian inversion framework for probabilistic inversion of EM data, which is an open-source software package implemented in the Julia programming language. The key feature of the framework is that it allows the model complexity to be adaptively adjusted to an appropriate level compatible with the data by implementing a reversible jump Markov chain Monte Carlo algorithm, thus allowing the data to infer the appropriate level of model complexity and associated parameter uncertainty. The authors have elaborated the structure of the package with a focus on code modularity and extensibility. Finally, the authors determine the capacity and versatility of the software package through three synthetic examples that simulate different EM scenarios. The inversion results demonstrate the performance and inherent resolving abilities of different EM surveys for conductive and/or resistive structures. In addition, the model ensemble produced by the transdimensional Bayesian inversion conveys a wealth of information. Many important quantities for data interpretation such as parameter uncertainty and correlation between model parameters of interest can be measured by exploring the model ensemble.

Fourier Subspace-Based Deep Learning Method for Inverse Design of Frequency Selective Surface

Frequency selective surface (FSS) is critical for electromagnetic (EM) radiation protection due to its high spatial filtering performance, especially for active FSS. Recently, the artificial neural network (ANN) has shown great potential in solving EM inverse problems and rapid industrial design. In such an inverse model with ANN, it establishes the relationship between the given inputs of S-parameters and the desired structure parameters or material parameters. However, faced with applications where S-parameters vary in a large frequency range with different curve shapes, such as multiband microwave devices, equal interval sampling may result in high-dimensional inputs and will require a more complicated neural network. In this work, we present a Fourier subspace-based deep learning method (FS-BDLM) for FSS inverse design, where the dimension of the input is largely reduced by using Fourier subspace to represent the most salient features of the desired S-parameter performance. Compared with existing deep learning methods, the proposed technique makes inverse neural models more compact and more stable to noise contaminations. The validation of the proposed FS-BDLM is conducted both numerically and experimentally through two dual-passband FSS design examples, where the well-designed FSS is fabricated to validate the technique.

Stability for the electromagnetic inverse source problem in inhomogeneous media

Abstract This paper is concerned with the stability of the inverse source problem for Maxwell’s equations in an inhomogeneous background medium. We show that the stability estimate consists of the Lipschitz-type data discrepancy and the high frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases. The analysis employs scattering theory to obtain the holomorphic domain and an upper bound for the resolvent of the elliptic operator.

The Incident Field Optimization Method for the Electromagnetic Inverse Problems

In this letter, an incident field optimization (IO) method integrated with contrast source inversion (CSI) method and multiplicative regularized CSI (MR-CSI) method is proposed to deal with the electromagnetic inverse problems. For the conventional iterative inversion methods, the incident field is a prior knowledge and is usually obtained by the calibration process. Through the synthetic data experiments, it can be found that a small distortion of the incident field has little impact on the inversion results, but a high distortion will lead to fault inversion results or no convergence. In this letter, the incident field optimal factor, being updated during the iterative process, is introduced into the CSI and MR-CSI method, named as IO-CSI and MR–IO–CSI. The new methods have good inversion performance even with high incident field distortion. The proposed methods are applied to the Fresnel experiment data directly without the calibration procedure. Both the single-frequency and multifrequency inversion experiments demonstrate that the IO-CSI and MR–IO–CSI method can achieve good inversion results, indicating the method’s practical applicability.

Deep Neural Network with Data Cropping Algorithm for Absorptive Frequency‐Selective Transmission Metasurface

AbstractDeep neural networks (DNNs) are widely used in designing a metasurface; however, data acquisition from simulations is expensive in terms of time and effort. Inspired by image cropping, a data cropping algorithm is proposed that can significantly reduce the simulation time required in the DNN pre‐training process. The algorithm crops the simulated data and adds random data to augment the amount of the dataset. By applying the proposed target‐driven DNN, an absorptive frequency‐selective transmission (AFST) metasurface structure with a low profile and a broad transmission band is designed. A transmission band from 7.5 to 14 GHz and an absorption rate as large as 0.75 beyond the transmission band are observed. The proposed method provides an efficient strategy to design metasurfaces and a fast solution to the electromagnetic inverse design problem.