基于多水平集的物理驱动神经网络求解三维逆散射问题
Multi-Level-Set-Based Physics-Driven Neural Network to Solve 3-D Inverse Scattering Problems
- Northwestern Polytechnical University（西北工业大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
提出基于多水平集的物理驱动神经网络LSPDNN，通过软联合多材料模型和TV正则化，解决三维电磁逆散射中的边界模糊和伪影问题，实现清晰、均匀的重建。
中文摘要 AI 辅助
本文提出了一种基于水平集的物理驱动神经网络求解器（LSPDNN），用于三维电磁逆散射问题。为缓解逐体素对比度重建中的边界模糊和重建伪影，所提出的求解器利用实际散射体的分段均匀性，通过多个坐标相关的神经水平集分量来表示未知目标。具体而言，提出了一种软联合多材料模型，以分别描述目标支撑和材料分布。全局支撑由多个水平集分量的并集形成，而局部对比度由归一化的分量权重和可学习的复介电常数候选值决定。此外，对材料区域指示器施加模型一致的总体变差（TV）正则化，而非直接施加于重建对比度，以抑制碎片化的材料分配，同时避免过度平滑材料界面。进一步引入自适应损失平衡策略，以减少对人工选择正则化权重的依赖。对于每个测量实例，通过最小化物理一致的目标函数来优化神经水平集参数和材料候选值。数值和实验结果表明，LSPDNN能够重建具有清晰边界、更均匀材料区域和显著减少背景伪影的散射体。结果突显了神经水平集参数化在涉及不规则形状、紧密间隔物体、多种材料和测量噪声的挑战性三维逆散射情况中的优势。
英文摘要
This paper proposes a level-set-based physics-driven neural network solver (LSPDNN) for 3-D electromagnetic inverse scattering. To mitigate boundary blurring and reconstruction artifacts in voxel-wise contrast reconstruction, the proposed solver exploits the piecewise homogeneity of practical scatterers by representing unknown targets with multiple coordinate-dependent neural level-set components. Specifically, a soft-union multi-material model is proposed to separately describe the object support and material distribution. The global support is formed by the union of multiple level-set components, while the local contrast is determined by normalized component weights and learnable complex permittivity candidates. In addition, a model-consistent total variation (TV) regularization is imposed on the material-region indicators, rather than directly on the reconstructed contrast, to suppress fragmented material assignments without excessively smoothing material interfaces. An adaptive loss balancing strategy is further introduced to reduce the dependence on manually selected regularization weights. For each measurement instance, the neural level-set parameters and material candidates are optimized by minimizing a physics-consistent objective function. Numerical and experimental results demonstrate that LSPDNN can reconstruct scatterers with clear boundaries, more uniform material regions, and substantially reduced background artifacts. The results highlight the advantage of the neural level-set parameterization in challenging 3-D inverse scattering cases involving irregular shapes, closely spaced objects, multiple materials, and measurement noise.
