论文标题
在高对比度介质中恢复嵌入式电磁源的超级分辨率
Super-resolution in recovering embedded electromagnetic sources in high contrast media
论文作者
论文摘要
这项工作的目的是在电磁（EM）辐射源的时间反转成像中对预期的超分辨率现象进行严格的数学分析。众所周知，分辨率限制基本上取决于EM Green张量的相关背景的张量的清晰度。我们首先通过Lippmann-Schinginger代表公式建立了分辨率和材料参数与电源集成运算符的分解之间的密切联系。然后，我们对整体算子的光谱结构进行了深入的特征，以在一般有限域中获得其在高对比度状态下其分辨率的杆铅笔分解。对于球形结构域的特殊情况，我们提供了特征值和本征函数的一些定量渐近行为。这些数学发现将使我们能够对高对比度介质中EM源重建中的超分辨率进行简洁明了的说明。还提供了一些数值示例，以验证我们的主要理论结果。
The purpose of this work is to provide a rigorous mathematical analysis of the expected super-resolution phenomenon in the time-reversal imaging of electromagnetic (EM) radiating sources embedded in a high contrast medium. It is known that the resolution limit is essentially determined by the sharpness of the imaginary part of the EM Green's tensor for the associated background. We first establish the close connection between the resolution and the material parameters and the resolvent of the electric integral operator, via the Lippmann-Schwinger representation formula. We then present an insightful characterization of the spectral structure of the integral operator for a general bounded domain and derive the pole-pencil decomposition of its resolvent in the high contrast regime. For the special case of a spherical domain, we provide some quantitative asymptotic behavior of the eigenvalues and eigenfunctions. These mathematical findings shall enable us to provide a concise and rigorous illustration of the super-resolution in the EM source reconstruction in high contrast media. Some numerical examples are also presented to verify our main theoretical results.
