This is an excellent collection of articles for analysis, as they are from a cohesive research area (and often the same research group), showcasing a clear and consistent style for writing high-impact scientific papers in computational science and engineering.

Based on an analysis of the provided textbook chapter and research articles, here is a summary of their writing characteristics and a guide on the train of thought for composing a similar article.

Overall Train of Thought

The core logic follows a “funnel” structure, moving from a general problem to a specific solution and then back to general implications.

  1. Problem: What is the broad, important problem we are trying to solve? (e.g., Inverse Scattering Problems).
  2. Challenge: Why is this problem hard? What specific aspect makes it difficult? (e.g., It’s ill-posed, nonlinear, and becomes even harder with phaseless data).
  3. State of the Art: How have others tried to solve this? What are the existing methods and what are their limitations? (e.g., Traditional iterative methods are slow; early deep learning methods are “black boxes”).
  4. Our Idea (The Gap): We have a novel idea to overcome a specific limitation. (e.g., “We can inspire the neural network design with physics” or “We can quantify the uncertainty of the deep learning prediction”).
  5. Our Method (The Solution): This is exactly how our idea is implemented, mathematically and algorithmically.
  6. Proof: How do we prove our method works and is better than the state of the art? (e.g., Through carefully designed numerical experiments and quantitative metrics).
  7. Implications: What is the significance of our work? Why does it matter and what’s next? (e.g., Our method is faster, more accurate for challenging cases, and opens up new research directions).

Breakdown by Section

Here is how this train of thought is structured in each part of the paper.

1. Abstract

The abstract is a highly condensed version of the entire paper, following a strict formula.

  • Starts with: A single sentence establishing the context and the primary challenge.
    • Example: “Reconstructing the exact electromagnetic property of unknown targets from the measured scattered field is challenging due to the intrinsic nonlinearity and ill-posedness.”
  • The “Gap” and “Our Proposal”: Immediately state what is missing and what you are proposing to fix it.
    • Example: “In this article, a new scheme, named the modified contrast scheme (MCS), is proposed to tackle nonlinear inverse scattering problems (ISPs).”
  • Core Technical Idea: Briefly state the key mechanism of your method.
    • Example: “A local-wave amplifier coefficient is used to form the modified contrast, which is able to alleviate the global nonlinearity…”
  • Key Result & Validation: Summarize the main finding from your experiments.
    • Example: “The numerical results show that MCS with the modified contrast input performs well in both 2-D and 3-D testing examples…”
  • Concluding Impact: A final sentence on why this is a significant improvement.
    • Example: “…a significant improvement is achieved in reconstructing high-contrast scatterers.”

2. Introduction

The introduction expands the abstract into a full narrative that guides the reader from the general field to your specific contribution.

  • Starts with (The Broad Funnel Opening): A broad statement about the importance and application of the field.
    • Example: “Electromagnetic inverse scattering problems (ISPs) are aimed at determining the nature of unknown scatterer… and have wide applications in the fields of nondestructive evaluation, geophysics, biomedical imaging…”
  • Defining the Challenge: Explain in more detail why the problem is difficult (nonlinearity, ill-posedness, computational cost, challenges of phaseless data). This educates the reader and sets the stage for why new methods are needed.
  • Literature Review (State of the Art): Systematically review existing categories of solutions.
    • Start with traditional methods (e.g., iterative solvers like DBIM, CSI, SOM) and state their pros and cons (e.g., physically grounded but slow).
    • Move to more recent approaches (e.g., early machine learning, deep learning) and state their pros and cons (e.g., fast but often “black boxes” lacking generalization).
  • Identifying the Specific Gap: Explicitly state the limitation in the state-of-the-art that your work will address. This is the most crucial part of the introduction.
    • Example: “However, little attention has been paid to the uncertainty quantification of these deep-learning methods…” or “In [29], the similarities between the iterative method… and the architecture of ANN have also been examined, which inspires to propose…”
  • Stating Your Contribution (The “Here We Show” Moment): Clearly and concisely list your paper’s contributions. Use a bulleted or numbered list for maximum clarity.
    • Example: “The main contributions of the proposed method are threefold. First… Second… Third…”
  • Paper Roadmap: End with a brief outline of the rest of the paper.
    • Example: “The structure of this article is as follows. Section II presents the formulation… Section III shows the numerical comparison…”

3. Methods (Formulation / Methodology)

This section is the technical core. The goal is precision and clarity, allowing another expert to understand and replicate your work.

  • Starts with the Foundation: Begin with the established physics and mathematical model (e.g., the Lippmann–Schwinger equation, the state and data equations). Define all terms, variables, and operators.
    • Example: “In ISPs, the forward model can be formulated by the following two discretized equations…”
  • Connecting to Your Idea: Bridge the foundational theory to your novel concept. Explain the high-level idea before diving into the mathematical details.
    • Example: “Inspired by contrast-source type iterative inversion solvers… we turn our attention from directly regressing contrast to the problem of estimating induced current…”
  • Detailing the Novelty: Provide a step-by-step derivation of your method. Use equations, algorithms (in pseudo-code), and diagrams (especially for neural network architectures). Justify your design choices.
    • Example: When describing a new input for a neural network, explain why that input is physically meaningful and more suitable than previous approaches (e.g., “The new constant value β₀ for the input generation provides us a freedom to control the performance of the U-Net.”).
  • Final Output Formulation: Clearly state how the final result (e.g., the reconstructed image) is obtained from your method’s output.

4. Numerical Results / Experiments

This section provides the evidence. The structure is methodical and focused on comparing your method against relevant benchmarks.

  • Starts with the Setup: Describe the simulation or experiment configuration in detail. This is critical for reproducibility.
    • Example: “In the numerical tests, we consider a DOI D with the size of 2 × 2 m² and discretize the domain into 64 × 64 pixels. The operating frequency is 400 MHz…”
    • Specify training/testing data, noise levels, and the quantitative metrics you will use (e.g., Relative Error, SSIM).
  • Present Results by Case Study: Organize the results into distinct examples or tests. Each test should be designed to prove a specific point (e.g., performance on weak scatterers, performance on strong scatterers, generalization ability, robustness to noise).
  • Show, Don’t Just Tell: Use figures (reconstructed images) and tables (quantitative scores) extensively. The figures should always include the “Ground Truth” for visual comparison.
  • Interpret the Results: For each figure and table, add text that guides the reader’s interpretation.
    • Example: “As demonstrated in Fig. 5(c) and (d), some artifacts appear in the reconstruction… while MCSM still offers a satisfactory reconstruction result. The average Re… is listed in Table II.”

5. Discussion and Conclusion

This section zooms back out. It summarizes the work and explains its broader significance.

  • Starts with a Restatement: Begin by restating the problem and your proposed solution in a single paragraph.
    • Example: “In this article, an improved scheme, named MCS, is proposed to tackle nonlinear ISPs. Under the MCS, both 2-D and 3-D real-time reconstruction results are provided…”
  • Summarize Key Findings: Briefly reiterate the most important results and what they prove.
    • Example: “It is found that, although the network is trained with MNIST data set, it is able to solve general ISPs and outperforms SOM and DCS in reconstructing some challenging profiles.”
  • Discuss the “Why”: Explain why your method performed well. Connect the successful results back to the design features you described in the Methods section. This provides deeper insight.
    • Example: “One reason for the better performance of MCSM is that the range of the modified contrast is always between 0 and 1, which makes it more suitable to be the input of the U-Net.”
  • Acknowledge Limitations and Propose Future Work: Show that you have a critical understanding of your own work by mentioning its limitations and suggesting how the research could be extended in the future.
    • Example: “Although the proposed method quantitatively achieves significantly better results… there is still room for improvements considering the advantages that have been exhibited by some iterative algorithms that are specially designed to tackle highly nonlinear ISPs…”

By following this structured train of thought, you can create a clear, logical, and persuasive scientific article that effectively communicates your contribution to the field.

Abstract

Far-Field Approximation Learning Method for Millimeter-Wave Short-Range Imaging

一种毫米波短距离成像的远场近似学习方法

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Abstract — Based on the far-field approximations, a deep learning-based method is proposed for millimeter-wave shortrange imaging. By using convolutional neural networks, the distortions caused by the far-field approximations and limitedaperture measurements could be corrected. Dissimilar to traditional algorithms, the proposed method has no restrictions on the placements of the antenna arrays and single-frequency illuminations are sufficient for the generations of 3-D highresolution reflectivity maps. In addition, it is fast to generate the input of neural network since the algorithm is based on inverse Fourier transform, which is ideal for generating training dataset. The performance of the proposed method is verified using both synthetic and experimental data. It is also demonstrated that enlarging the k-space coverage, which can be accomplished by increasing the dimensions of the antenna arrays, can improve the resolution of the proposed method.

摘要——基于远场近似，提出了一种基于深度学习的毫米波短程成像方法。通过使用卷积神经网络，可以校正由远场近似和有限扰动测量引起的失真。与传统算法不同，该方法对天线阵列的放置没有限制，单频照明足以生成三维高分辨率反射率图。此外，由于该算法基于傅里叶逆变换，因此生成神经网络的输入很快，非常适合生成训练数据集。使用合成数据和实验数据验证了所提出方法的性能。还证明了通过增加天线阵列的尺寸来扩大k空间覆盖范围可以提高所提出方法的分辨率。

An Improved Deep Learning Scheme for Solving 2-D and 3-D Inverse Scattering Problems

一种用于求解二维和三维逆散射问题的改进深度学习方案

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Abstract— Reconstructing the exact electromagnetic property of unknown targets from the measured scattered field is challenging due to the intrinsic nonlinearity and ill-posedness. In this article, a new scheme, named the modified contrast scheme (MCS), is proposed to tackle nonlinear inverse scattering problems (ISPs). A local-wave amplifier coefficient is used to form the modified contrast, which is able to alleviate the global nonlinearity in original ISPs without decreasing the accuracy of the problem formulation. Moreover, the modified contrast is more suitable to be the input of the deep learning scheme, due to the unity bound of the modified contrast. The numerical results show that MCS with the modified contrast input performs well in both 2-D and 3-D testing examples in real time after offline training process, even in high-relative-permittivity cases. Compared with the dominant current scheme, a significant improvement is achieved in reconstructing high-contrast scatterers.

摘要——由于固有的非线性和病态性，从测量的散射场中重建未知目标的精确电磁特性具有挑战性。本文提出了一种名为改进对比度方案（MCS）的新方案来解决非线性逆散射问题（ISP）。使用局域波放大器系数来形成修改后的对比度，这能够在不降低问题公式精度的情况下缓解原始ISP中的全局非线性。此外，由于修正对比度的统一界限，修正对比度更适合作为深度学习方案的输入。数值结果表明，在离线训练过程后，具有修改对比度输入的MCS在二维和三维测试示例中实时表现良好，即使在高相对电容率的情况下也是如此。与主流方案相比，在重建高对比度散射体方面取得了显著改进。

MUSIC Imaging and Electromagnetic Inverse Scattering of Multiple-Scattering Small Anisotropic Spheres

多散射小各向异性球体的MUSIC成像和电磁逆散射

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Abstract—The Foldy-Lax equation is used to derive a multiple scattering model for the multiple-scattering small anisotropic spheres. By this model, if the number of the non-zero singular values of the multistatic response (MSR) matrix is smaller than the number of the antennas, the range space of the MSR matrix is found to be spanned by the background Green’s function vectors corresponding to the and components of the electric and magnetic dipoles induced in each scatterer, which indicates that the multiple signal classification (MUSIC) method could be implemented to obtain the locations of the scatterers. After estimating the positions of the scatterers, a non-iterative analytical method is proposed for retrieving the polarization strength tensors as well as the orientations of the principle axes of each scatterer. Two numerical simulations show that, the MUSIC method and the non-iterative method are efficacious for the nonlinear inverse scattering problem of determining the locations and polarization strength tensors of multiple-scattering small anisotropic spheres. Such methods could also be applied to the inversion of small isotropic spheres or extended to the inversion of small bianisotropic spheres.

摘要——利用Foldy-Lax方程推导了多散射小各向异性球体的多散射模型。通过该模型，如果多稳态响应（MSR）矩阵的非零奇异值的数量小于天线的数量，则发现MSR矩阵的距离空间由与每个散射体中感应的电偶极子和磁偶极子的分量对应的背景格林函数向量跨越，这表明可以实现多信号分类（MUSIC）方法来获得散射体的位置。在估计散射体的位置后，提出了一种非迭代分析方法来反演极化强度张量以及每个散射体主轴的方向。两个数值模拟表明，MUSIC方法和非迭代方法对于确定多散射小各向异性球体的位置和极化强度张量的非线性逆散射问题是有效的。这种方法也可以应用于小各向同性球体的反演，或扩展到小双各向异性球体的反演。

Deep Learning-Based Inversion Methods for Solving Inverse Scattering Problems With Phaseless Data

基于深度学习的求解无相位数据逆散射问题的反演方法

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Abstract— Without phase information of the measured field data, the phaseless data inverse scattering problems (PD-ISPs) counter more serious nonlinearity and ill-posedness compared with full data ISPs (FD-ISPs). In this article, we propose a learning-based inversion approach in the frame of the U-net convolutional neural network (CNN) to quantitatively image unknown scatterers located in homogeneous background from the amplitude-only measured total field (also denoted PD). Three training schemes with different inputs to the U-net CNN are proposed and compared, i.e., the direct inversion scheme (DIS) with phaseless total field data, retrieval dominant induced currents by the Levenberg–Marquardt (LM) method (PD-DICs), and PD with contrast source inversion (PD-CSI) scheme. We also demonstrate the setup of training data and compare the performance of the three schemes using both numerical and experimental tests. It is found that the proposed PD-CSI and PD-DICs perform better in terms of accuracy, generalization ability, and robustness compared with DIS. PD-CSI has the strongest capability to tackle with PD-ISPs, which outperforms the PD-DICs and DIS.

摘要——在没有实测场数据相位信息的情况下，无相位数据逆散射问题（PD ISP）与全数据ISP（FD ISP）相比，具有更严重的非线性和病态性。在这篇文章中，我们提出了一种在U-net卷积神经网络（CNN）框架下的基于学习的反演方法，从仅测量振幅的总场（也称为PD）中定量成像位于均匀背景中的未知散射体。提出并比较了U-net CNN的三种不同输入的训练方案，即无相位全场数据的直接反演方案（DIS）、Levenberg-Marquardt（LM）方法反演主导感应电流（PD-DIC）和PD对比源反演（PD-CSI）方案。我们还演示了训练数据的设置，并使用数值和实验测试比较了三种方案的性能。研究发现，与DIS相比，所提出的PD-CSI和PD-DIC在准确性、泛化能力和鲁棒性方面表现更好。PD-CSI在处理PD-ISP方面具有最强的能力，其性能优于PD-DIC和DIS。

Uncertainty Quantification in Inverse Scattering Problems With Bayesian Convolutional Neural Networks

贝叶斯卷积神经网络在逆散射问题中的不确定性量化

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Abstract— Recently, tremendous progress has been achieved in applying deep learning schemes (DLSs) to solve inverse scattering problems (ISPs), where state-of-the-art performance has been attained. However, little attention has been paid to the uncertainty quantification of these deep-learning methods in solving ISPs. In other words, the error of the prediction is not known since the ground truth is not available in practice. In this article, a Bayesian convolutional neural network (BCNN) is used to quantify the uncertainties in solving ISPs. With Monte Carlo dropout, the proposed BCNN is able to directly predict the pixel-based uncertainties of the widely used DLSs in ISPs. To quantitatively evaluate the performance of uncertainty predictions, both correlation coefficient and nonlinear correlation distribution between the predicted uncertainty and true absolute error are calculated. The tests on both synthetic and experimental data show that the predictive uncertainty is highly correlated with true absolute error calculated from the ground truth. Besides, when DLSs fail to solve an ISP, the predicted uncertainty increases significantly, which offers a pixel-based “confidence level” in solving ISPs.

摘要——最近，在应用深度学习方案（DLS）解决逆散射问题（ISP）方面取得了巨大进展，取得了最先进的性能。然而，很少有人关注这些深度学习方法在解决ISP问题时的不确定性量化。换句话说，由于在实践中无法获得地面真相，因此预测的误差是未知的。本文使用贝叶斯卷积神经网络（BCNN）来量化求解ISP时的不确定性。在蒙特卡洛丢弃的情况下，所提出的BCNN能够直接预测ISP中广泛使用的DLS的基于像素的不确定性。为了定量评估不确定性预测的性能，计算了预测不确定性与真实绝对误差之间的相关系数和非线性相关分布。对合成数据和实验数据的测试表明，预测不确定度与根据地面真实值计算的真实绝对误差高度相关。此外，当DLS无法解决ISP时，预测的不确定性会显著增加，这为解决ISP提供了基于像素的“置信水平”。

Physics-Inspired Convolutional Neural Network for Solving Full-Wave Inverse Scattering Problems

求解全波逆散射问题的物理启发卷积神经网络

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Abstract— In this paper, to bridge the gap between physical knowledge and learning approaches, we propose an induced current learning method (ICLM) by incorporating merits in traditional iterative algorithms into the architecture of convolutional neural network (CNN). The main contributions of the proposed method are threefold. First, to the best of our knowledge, it is the first time that the contrast source is learned to solve full-wave inverse scattering problems (ISPs). Second, inspired by the basis-expansion strategy in the traditional iterative approach for solving ISPs, a combined loss function with multiple labels is defined in a cascaded end-to-end CNN (CEE-CNN) architecture to decrease the nonlinearity of objective function, where no additional computational cost is introduced in generating extra labels. Third, to accelerate the convergence speed and decrease the difficulties of the learning process, the proposed CEE-CNN is designed to focus on learning the minor part of the induced current by introducing several skip connections and to bypass the major part of induced current to the output layers. The proposed method is compared with the state-of-the-art of deep learning scheme and a well-known iterative ISP solver, where numerical and experimental tests are conducted to verify the proposed ICLM.

摘要——为了弥合物理知识和学习方法之间的差距，本文将传统迭代算法的优点融入卷积神经网络（CNN）的架构中，提出了一种感应电流学习方法（ICLM）。该方法的主要贡献有三方面。首先，据我们所知，这是第一次学习对比源来解决全波逆散射问题（ISP）。其次，受求解ISP的传统迭代方法中的基扩展策略的启发，在级联的端到端CNN（CEE-CNN）架构中定义了一个具有多个标签的组合损失函数，以降低目标函数的非线性，其中在生成额外标签时不引入额外的计算成本。第三，为了加快收敛速度并降低学习过程的难度，所提出的CEE-CNN被设计为通过引入几个跳跃连接来专注于学习感应电流的较小部分，并将感应电流的主要部分绕过输出层。将提出的方法与最先进的深度学习方案和著名的迭代ISP求解器进行了比较，在那里进行了数值和实验测试来验证提出的ICLM。

Precise Near-Range 3-D Image Reconstruction Based on MIMO Circular Synthetic Aperture Radar

基于MIMO圆形合成孔径雷达的精确近距离三维图像重建

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Abstract— This article studies the near-range 3-D image reconstruction based on millimeter-wave multiple-input-multipleoutput circular synthetic aperture radar (MIMO-CSAR). We first derive the exact forward wave model of MIMO-CSAR and then propose a range migration algorithm for near-range high-precision 3-D image reconstruction. Our formulation is strictly based on wave theory. The propagation attenuation, which is an inherent factor in wave equation and is significant for near-range wide-angle sensing case, is considered and compensated efficiently with a Fourier-domain matched filtering. Besides, the phase decoupling is achieved with a 2-D Stolt mapping. The computational complexity of the algorithm is at the same level as the state-of-the-art method. Compared with the state of the art, by considering the amplitude variation, the imaging quality can be improved for near-range measurement with large beamwidth. The results from both synthetic and practical measurement data demonstrate that a wider dynamic range (less sidelobes appeared at the same dynamic level) and a better recovery for widespread targets compared with the state-of-the-art imaging method.

摘要——本文研究了基于毫米波多输入多输出圆合成孔径雷达（MIMO-CSAR）的近距离三维图像重建。我们首先推导了MIMO-CSAR的精确前向波模型，然后提出了一种用于近距离高精度三维图像重建的距离偏移算法。我们的公式严格基于波动理论。传播衰减是波动方程中的一个固有因素，对近距离广角传感情况具有重要意义，通过傅里叶域匹配滤波有效地考虑和补偿了传播衰减。此外，通过二维斯托尔特映射实现了相位解耦。该算法的计算复杂度与最先进的方法处于同一水平。与现有技术相比，通过考虑振幅变化，可以提高大波束宽度近距离测量的成像质量。合成和实际测量数据的结果表明，与最先进的成像方法相比，该方法具有更宽的动态范围（在相同的动态水平下出现的旁瓣更少）和对广泛目标的更好恢复。

Learning-Based Fast Electromagnetic Scattering Solver Through Generative Adversarial Network

基于生成对抗网络的快速电磁散射求解器

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Abstract— This article proposes a learning-based noniterative method to solve electromagnetic (EM) scattering problems utilizing pix2pix, a popular generative adversarial network (GAN). Instead of calculating induced currents directly from a matrix inversion, a forward-induced current learning method (FICLM) is introduced to calculate the induced current through a neural-network mapping. The scattered fields can be further calculated through a multiplication of the Green’s function with the predicted induced currents. Inspired by wave physics of scattering problems, we have designed three kinds of input schemes, covering different combinations of the given incident field and permittivity contrast, to evaluate the performance of the FICLM model under both single-incidence and multi-incidence cases. Numerical results prove that the proposed FICLM outperforms the method of moments (MoM) in terms of both computational speed and accuracy by use of reference data with a higher precision. The FICLM with the direct sum of permittivity contrast and a so-called Born-type induced current, achieves the best calculation accuracy and generalization capability compared to the other two inputs. The comparison with other types of neural networks, such as U-net, also demonstrates the superior performance of FICLM for dealing with complex scatterers due to the use of adversarial framework in pix2pix. The proposed method paves a new way for the fast solution of EM-scattering problems through deep learning techniques.

摘要——本文提出了一种基于学习的非迭代方法，利用流行的生成对抗网络（GAN）pix2pix来解决电磁（EM）散射问题。引入正向感应电流学习方法（FICLM），通过神经网络映射计算感应电流，而不是直接从矩阵求逆计算感应电流。通过将格林函数与预测的感应电流相乘，可以进一步计算散射场。受散射问题的波动物理学的启发，我们设计了三种输入方案，涵盖了给定入射场和介电常数对比度的不同组合，以评估FICLM模型在单入射和多入射情况下的性能。数值结果证明，通过使用具有更高精度的参考数据，所提出的FICLM在计算速度和精度方面都优于矩量法（MoM）。与其他两个输入相比，具有电容率对比度和所谓的玻恩型感应电流的直接和的FICLM实现了最佳的计算精度和泛化能力。与其他类型的神经网络（如U-net）的比较也表明，由于在pix2pix中使用了对抗框架，FICLM在处理复杂散射体方面具有优越的性能。该方法为利用深度学习技术快速求解电磁散射问题开辟了新途径。