基于拓扑导数的技术用于用少量入射方向成像薄不均匀体
Topological derivative-based technique for imaging thin inhomogeneities with few incident directions
AI总结：
本文提出一种基于拓扑导数的成像技术，通过分析数学结构证明少量入射方向即可有效成像薄不均匀体，并探讨最优方向配置。
摘要：
许多非迭代成像算法需要大量入射方向。基于拓扑导数的成像技术可缓解此问题，但缺乏理论背景和选择最优入射方向的明确方法。本文严格分析拓扑导数成像函数的数学结构，确认为何少量入射方向足够，并探索这些方向的最优配置。为此，我们将基于拓扑导数的成像函数表示为无穷级数中的整数阶第一类贝塞尔函数。我们的分析通过数值模拟结果得到支持。
英文摘要：
Many non-iterative imaging algorithms require a large number of incident directions. Topological derivative-based imaging techniques can alleviate this problem, but lacks a theoretical background and a definite means of selecting the optimal incident directions. In this paper, we rigorously analyze the mathematical structure of a topological derivative imaging function, confirm why a small number of incident directions is sufficient, and explore the optimal configuration of these directions. To this end, we represent the topological derivative based imaging function as an infinite series of Bessel functions of integer order of the first kind. Our analysis is supported by the results of numerical simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
