理想导电弧形裂纹成像的多频子空间偏移
Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks
摘要：
在逆散射问题中，对于混凝土墙或桥梁裂缝、地下杀伤人员地雷等未知电磁目标的非迭代成像，通常采用多频子空间偏移成像技术。它被证实，这种技术是非常快速，有效的，强大的，并可以应用不仅全视图，但也有限的视图反问题，如果适当数量的入射和相应的散射场的应用和收集。但在许多作品中，这种技术的应用是某种启发式的。在这种启发式应用的动机下，本文分析了二维逆散射子空间迁移成像技术中的成像泛函的结构，当未知目标是位于均匀二维空间中的任意形状的弧形理想导电裂纹时。与基于统计假设检验的统计方法相反，我们的方法是基于这样一个事实，即子空间偏移成像泛函可以表示为第一类整数阶贝塞尔函数的线性组合。这是基于在横磁（TM）模式或横电（TE）模式下以非零频率在远场中收集的多静态响应（MSR）矩阵的结构。探讨了成像泛函的表达式，给出了子空间偏移的某些性质，回答了多频成像提高分辨率的原因。特别地，我们仔细地分析了子空间迁移，并确认了一些性质的成像时，施加少量的入射场。因此，我们简单地介绍了加权多频成像泛函，并确认这是一个改进的版本的子空间偏移TM模式。
英文摘要：
Multi-frequency subspace migration imaging technique are usually adopted for the non-iterative imaging of unknown electromagnetic targets such as cracks in the concrete walls or bridges, anti-personnel mines in the ground, etc. in the inverse scattering problems. It is confirmed that this technique is very fast, effective, robust, and can be applied not only full- but also limited-view inverse problems if suitable number of incident and corresponding scattered field are applied and collected. But in many works, the application of such technique is somehow heuristic. Under the motivation of such heuristic application, this contribution analyzes the structure of imaging functional employed in the subspace migration imaging technique in two-dimensional inverse scattering when the unknown target is arbitrary shaped, arc-like perfectly conducting cracks located in the homogeneous two-dimensional space. Opposite to the Statistical approach based on the Statistical Hypothesis Testing, our approach is based on the fact that subspace migration imaging functional can be expressed by a linear combination of Bessel functions of integer order of the first kind. This is based on the structure of the Multi-Static Response (MSR) matrix collected in the far-field at nonzero frequency in either Transverse Magnetic (TM) mode or Transverse Electric (TE) mode. Explored expression of imaging functionals gives us certain properties of subspace migration and an answer of why multi-frequency enhances imaging resolution. Particularly, we carefully analyze the subspace migration and confirm some properties of imaging when a small number of incident field is applied. Consequently, we simply introduce a weighted multi-frequency imaging functional and confirm that which is an improved version of subspace migration in TM mode.
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