基于算子反演与匹配滤波的近场微波成像中线性化逆散射问题求解
图像与视频处理
2024-12-23 v2
摘要
微波成像通常基于匹配滤波算法求解线性化逆散射问题，即对观测数据施加正 scattering 算子的伴随算子。更严谨的方法是显式反演正 scattering 算子，本文针对准单体成像场景，依据 Weyl 同一式和层次加速算法构建平面平面波表示，实现该反演。通过正则化迭代线性方程组求解器实现反演，支持不规则观测数据以及完整探头校正。在空间图像生成过程中，可采用低通滤波以减少成像伪影。本文还引入相应的谱反投影算法和空间反投影算法，并构建改进的聚焦算子。对比分析了各种示例（包括模拟数据和测量数据）下的图像生成算法。结果表明，逆源解在鲁棒性、聚焦能力和图像精度方面优于在空间或谱域上运行的伴随成像算法。这一结论在不规则采样网格、非理想或被截断观测数据情形下尤为明显，且通过严格的定量分析评估了所有重建结果。
引用
@article{arxiv.2410.06465,
title = {On the Solution of Linearized Inverse Scattering Problems in Near-Field Microwave Imaging by Operator Inversion and Matched Filtering},
author = {Matthias M. Saurer and Han Na and Marius Brinkmann and Thomas F. Eibert},
journal= {arXiv preprint arXiv:2410.06465},
year = {2024}
}
备注
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