Electromagnetic Inverse Scattering Research Articles

Enhanced Deep Learning Approach Based on the Conditional Generative Adversarial Network for Electromagnetic Inverse Scattering Problems

Enhanced Deep Learning Approach Based on the Conditional Generative Adversarial Network for Electromagnetic Inverse Scattering Problems

A Physics-Induced Deep Learning Scheme for Electromagnetic Inverse Scattering

A Physics-Induced Deep Learning Scheme for Electromagnetic Inverse Scattering

Attention-Unet for Electromagnetic Inverse Scattering Problems in Microwave Imaging

Attention-Unet for Electromagnetic Inverse Scattering Problems in Microwave Imaging

A Hybrid Forward-Inverse Neural Network With the Transceiver-Configuration-Independent Technique for the Wideband Electromagnetic Inverse Scattering Problem

A Hybrid Forward-Inverse Neural Network With the Transceiver-Configuration-Independent Technique for the Wideband Electromagnetic Inverse Scattering Problem

Cross-Correlated Subspace-Based Optimization Method for Solving Electromagnetic Inverse Scattering Problems

Cross-Correlated Subspace-Based Optimization Method for Solving Electromagnetic Inverse Scattering Problems

A Novel Analysis of Super-Resolution for Born-Iterative-Type Algorithms in Microwave Medical Sensing and Imaging.

Microwave medical sensing and imaging (MMSI) is a highly active research field. In MMSI, electromagnetic inverse scattering (EIS) is a commonly used technique that infers the internal characteristics of the diseased area by measuring the scattered field. It is worth noting that the image formed by EIS often exhibits the super-resolution phenomenon, which has attracted much research interest over the past decade. A classical perspective is that multiple scattering leads to super-resolution, but this is subject to debate. This paper aims to analyze the super-resolution behavior for Born-iterative-type algorithms for the following three aspects. Firstly, the resolution defined by the traditional Rayleigh criterion can only be applied to point scatterers. It does not suit general scatterers. By using the Sparrow criterion and the generalized spread function, the super-resolution condition can be derived for general scatterers even under the Born approximation (BA) condition. Secondly, an iterative algorithm results in larger coefficients in the high-frequency regime of the optical transfer function compared to non-iterative BA. Due to the anti-apodization effect, the spread function of the iterative method becomes steeper, which leads to a better resolution following the definition of the Sparrow criterion mentioned above. Thirdly, the solution from the previous iteration, as the prior knowledge for the next iteration, will cause changes in the total field, which provides additional information outside the Ewald sphere and thereby gives rise to super-resolution. Comprehensive numerical examples are used to verify these viewpoints.

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.

Quantitative Analysis of Super Resolution in Electromagnetic Inverse Scattering for Microwave Medical Sensing and Imaging.

Microwave medical sensing and imaging (MMSI) has been a research hotspot in the past years. Imaging algorithms based on electromagnetic inverse scattering (EIS) play a key role in MMSI due to the super-resolution phenomenon. EIS problems generally employ far-field scattered data to reconstruct images. However, the far-field data do not include information outside the Ewald's sphere, so theoretically it is impossible to achieve super resolution. The reason for super resolution has not been clarified. The majority of the current research focuses on how nonlinearity affects the super-resolution phenomena in EIS. However, the mechanism of super-resolution in the absence of nonlinearity is routinely ignored. In this research, we address a prevalent yet overlooked problem where the image resolution due to scatterers of extended structures is incorrectly analyzed using the model of point scatterers. Specifically, the classical resolution of EIS is defined by the Rayleigh criterion which is only suitable for point-like scatterers. However, the super-resolution in EIS is often observed for general scatterers like cylinders, squares or Austria shapes. Subsequently, we provide theoretical results for the Born approximation framework in EIS, and employ the Sparrow criteria to quantify the resolution for symmetric objects of extended structures. Furthermore, the modified Sparrow criterion is proposed to calculate the resolution of asymmetric scatterers. Numerical examples show that the proposed approach can better explain the super-resolution phenomenon in EIS.

A Mesh-Free 3-D Deep Learning Electromagnetic Inversion Method Based on Point Clouds

Deep learning has been successfully used in the 2-D-mesh-based electromagnetic inverse scattering (EMIS) problems in the past. However, for 3-D EMIS problems, the massive amount of meshes generated by the mesh-based inversion methods makes deep learning implementation very challenging. Addressing this challenge will facilitate the further development of deep learning for 3-D EMIS problems. Inspired by the idea of point cloud, we propose a novel 3-D deep learning inversion methodology in this article. Different from previous work, the introduction of point clouds obviates the need to mesh the domain of interest (DOI) in this method, so we call it a mesh-free inversion method. The major advantage of this method compared with the mesh-based inversion methods is the low computational cost. In addition, the proposed method has other advantages. First, differently from prior deep learning inversion methods, the use of a reversible deep neural network (DNN) enables the proposed method to tackle both EMIS and electromagnetic forward scattering (EMFS) computations. Second, the inversion process becomes more controllable in this method, i.e., we can reconstruct merely a portion of the scatterer by simply shrinking the DOI. Third, the number of points used for the inversion can also be set as desired, without depending on the computational resources. Numerical and measured experiments demonstrate the feasibility and efficiency of the proposed method. This work opens a new vista on the application of deep learning toward 3-D EMIS problems. The code will be available at https://github.com/PKU-EMSensingLab/A-mesh-free-inversion-method-based-on-point-clouds.

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.

Enhanced Two-Step Deep-Learning Approach for Electromagnetic-Inverse-Scattering Problems: Frequency Extrapolation and Scatterer Reconstruction

The electromagnetic-inverse-scattering (EMIS) problem is solved by a novel two-step deep-learning (DL) approach in this article. The newly proposed two-step DL approach not only predicts the multifrequency EM scattered field, but also overcomes the limitation of the conventional methods for solving EMIS problems, such as expensive computational cost, strong ill-conditions, and invalidity on high contrast. In the first step, the complex-valued deep residual convolutional neural network (DRCNN) is utilized to predict multifrequency EM scattered fields only using single-frequency EM scattered field information. Based on a new complex-valued deep convolutional encoder-decoder (DCED) structure, the second step utilizes the obtained multifrequency EM scattered field “images” to realize the reconstruction of the target scatterers. In such a manner, the proposed approach can solve the EMIS problem accurately and efficiently even for inhomogeneous and high-contrast scatterers. The training of the proposed two DL models is based on the simple synthetic dataset. Numerical examples based on various dielectric objects are given to demonstrate the accuracy and performance of the newly proposed approach. The proposed DL-based method opens a new path for handling real-time quantitative microwave imaging.

Towards Intelligent Electromagnetic Inverse Scattering Using Deep Learning Techniques and Information Metasurfaces

Electromagnetic inverse scattering (EMIS) is uniquely positioned among many inversion methods because it enables to image the scene in a contactless, quantitative and super-resolution way. Although many EMIS approaches have been proposed to date, they usually suffer from two important challenges, i.e., time-consuming data acquisition and computationally -prohibitive data post processing, especially for large-scale objects with high and even moderate contrasts. To tackle the challenges, we here propose a framework of intelligent EMIS with the aid of deep learning techniques and information metasurfaces, enabling to the efficient data acquisition and instant data processing in a smart way. Towards this goal, as illustrative examples, we considerably extend the canonical contrast source inversion (CSI) algorithm, a canonical EMIS method by updating the contrast via the generative adversarial network (GAN), an unsupervised deep learning approach, leading to a novel physics-informed unsupervised deep learning method for EMIS, referred to as CSI-GAN in short. Compared with existing deep learning solutions for EMIS, our method relies on the supervision of physical law instead of the labeled training dataset, beating the bottleneck arising from the collection of labeled training datasets. Furthermore, we propose a scheme of adaptive data acquisition with the use of information metasurface in a cost-efficiency way, remarkably reducing the number of measurements and thus speeding up the data acquisition but maintaining the reconstruction's quality. Illustrative examples are provided to demonstrate the performance gain in terms of reconstruction quality, showing the promising potentials for providing the intelligent scheme for the EMIS problems.

Space-Time Electromagnetic Inverse Scattering Tomography of Objects With Affine Deformation

In this article, an electromagnetic inverse scattering problem (EISP) method is implemented successfully to capture the dynamic phenomena of the scene with affine deformation. In the presented method, a new variational model has been suggested which is based on two error functions of the current and state equations. Moreover, two types of regularizers have been adopted in the proposed scheme. In the first type, two separated spatial total variation (TV) and smooth, temporal regularization terms are used. In the second kind, a TV regularization, being a function of both spatial and temporal variables, is used. It is shown that the second type gives better results compared to the first type. The minimization problem is solved by the first-order primal-dual optimization algorithm of Chambolle and Pock.

Imaging of Insect Hole in Living Tree Trunk Based on Joint Driven Algorithm of Electromagnetic Inverse Scattering.

Trunk pests have always been one of the most important species of tree pests. Trees eroded by trunk pests will be blocked in the transport of nutrients and water and will wither and die or be broken by strong winds. Most pests are social and distributed in the form of communities inside trees. However, it is difficult to know from the outside if a tree is infected inside. A new method for the non-invasive detecting of tree interiors is proposed to identify trees eroded by trunk pests. The method is based on electromagnetic inverse scattering. The scattered field data are obtained by an electromagnetic wave receiver. A Joint-Driven algorithm is proposed to realize the electromagnetic scattered data imaging to determine the extent and location of pest erosion of the trunk. This imaging method can effectively solve the problem of unclear imaging in the xylem of living trees due to the small area of the pest community. The Joint-Driven algorithm proposed by our group can achieve accurate imaging with a ratio of pest community radius to live tree radius equal to 1:60 under the condition of noise doping. The Joint-Driven algorithm proposed in this paper reduces the time cost and computational complexity of tree internal defect detection and improves the clarity and accuracy of tree internal defect inversion images.

Probabilistic Deep Learning Solutions to Electromagnetic Inverse Scattering Problems Using Conditional Renormalization Group Flow

Deep learning (DL) has demonstrated great potential in solving nonlinear electromagnetic inverse scattering (EMIS) problems. However, the lack of uncertainty quantification and reliability assessment in the predictions remains an unresolved challenge. Overcoming this challenge is of critical importance in practice because of the presence of uncertainties and noise in the measurement data and the ill-posedness of EMIS problems. Here, we propose a conditional renormalization and generation-flow (cRG-Flow) network, a reversible hierarchical network, and develop a novel probabilistic DL strategy to quantify the uncertainty in DL solutions of EMIS problems. The proposed strategy provides two other important advantages over the existing DL approaches for solving EMIS problems. First, due to the reversible property of cRG-Flow, both the forward EM scattering computation and its inverse procedure can be considered simultaneously in the network and, as a result, physical constraints on the DL solutions can be easily imposed. Second, the interpretability of DL solutions is facilitated due to the utilization of RG-Flow. Illustrative examples are provided to demonstrate the performance gain in terms of reconstruction quality and robustness. The proposed method may pave a new avenue for addressing the EMIS problems based on DL schemes with improved reliability and interpretability.

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.

Learning-Based Inversion Method for Solving Electromagnetic Inverse Scattering With Mixed Boundary Conditions

In this article, a unified learning-based approach is introduced to solve inverse scattering problems (ISPs) with mixed boundary conditions (BCs). The scattering behavior of hybrid dielectric and perfect electric conductors (PEC) scatterers is modeled by the T-matrix method. A rough image of the zero-order T-matrix coefficients for unknown scatterers is first reconstructed by the backpropagation (BP) method, which is then refined by an attention-assisted pix2pix generative adversarial network (GAN). The spatial attention mechanism is utilized to enforce the generator network to learn salient features of the unknown scatterers instead of the background. The adversarial training of the generator and the discriminator further enables the reconstructed image to be constrained by high-level features of reference scatterers. Numerical tests on both synthetic and experimental data verify the superior performance of the proposed method for ISP reconstructions with hybrid scatterers. It effectively expands the application scope of learning-based ISP methods to reconstruct scatterers without knowing the BCs of scatterers in advance.

Multi‐model fusion approach for electromagnetic inverse scattering problems

In this paper, a novel deep learning (DL) approach is developed to solve the electromagnetic inverse scattering (EMIS) problems. Many challenges, such as ill-posedness, high computational cost, and strong non-linearity, are encountered when solving the EMIS problems. To surmount these difficulties, a multi-model fusion convolutional neural network architecture is proposed, termed here as Amplitude-Phase scheme. To the best of our knowledge, it is the first time that the multi-model fusion DL approach is employed to solve the EMIS problems. Amplitude data and phase data of the measured scattering data are applied to train the proposed scheme. Furthermore, we compare APs with three different training schemes, including Amplitude-Only scheme, and Phase-Only scheme, and Complex-Value scheme. The performance of the proposed DL schemes has been validated by numerical simulations. The results demonstrate that the proposed multi-model fusion approach outperforms other DL schemes in terms of accuracy and is able to achieve a better performance in reconstructing homogeneous and heterogeneous scatterers.

Fast Full-Wave Electromagnetic Inverse Scattering Based on Scalable Cascaded Convolutional Neural Networks

The end-to-end scalable cascaded convolutional neural networks (SC-CNNs) are proposed to solve inverse scattering problems (ISPs), and the high-resolution image can be directly obtained from the scattered field with the guiding by multiresolution labels in the cascaded blocks. To alleviate the difficulty of solving the ISPs via a full-wave way, the proposed SC-CNNs are physically decomposed into two parts, i.e., the linear transformation and the multiresolution imaging networks. The first part is composed of one CNN block and is used to mimic the linear transformation [e.g., backpropagation (BP)] from scattered field to the preliminary image, whereas the second part consists of a few cascaded CNN blocks to realize the reconstruction from the rough image to high-resolution image. With more high-frequency components incorporating into the multiresolution labels, the cascaded networks can be guided through those labels, avoiding black-box operations and enhancing the physical meaning and interpretability. The proposed SC-CNNs are verified by both the synthetic and experimental examples and it is proved that better performance can be achieved in terms of both inversion accuracy and efficiency compared to the BP-Unet and direct inversion scheme (DIS).

A Non-Iterative Method Combined with Neural Network Embedded in Physical Model to Solve the Imaging of Electromagnetic Inverse Scattering Problem

The main purpose of this paper is to solve the electromagnetic inverse scattering problem (ISP). Compared with conventional tomography technology, it considers the interaction between the internal structure of the scene and the electromagnetic wave in a more realistic manner. However, due to the nonlinearity of ISP, the conventional calculation scheme usually has some problems, such as the unsatisfactory imaging effect and high computational cost. To solve these problems and improve the imaging quality, this paper presents a simple method named the diagonal matrix inversion method (DMI) to estimate the distribution of scatterer contrast (DSC) and a Generative Adversarial Network (GAN) which could optimize the DSC obtained by DMI and make it closer to the real distribution of scatterer contrast. In order to make the distribution of scatterer contrast generated by GAN more accurate, the forward model is embedded in the GAN. Moreover, because of the existence of the forward model, not only is the DSC generated by the generator similar to the original distribution of the scatterer contrast in the numerical distribution, but the numerical of each point is also approximate to the original.