Engineering Computations ( IF 1.6 ) Pub Date : 2021-06-17 , DOI: 10.1108/ec-12-2020-0728 Lucas Fernandez 1 , Ravi Prakash 2
Purpose
The purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.
Design/methodology/approach
The method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.
Findings
In this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.
Originality/value
The current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.
中文翻译:
基于拓扑导数法的小可穿透障碍物成像
目的
本文的目的是提出基于拓扑导数的重建算法来解决可穿透障碍物的逆散射问题。
设计/方法/方法
该方法包括将逆重构问题重写为拓扑优化问题,然后使用拓扑导数的概念来寻求拓扑扰动成本泛函的高阶渐近展开。这种扩展被截断,然后相对于所考虑的参数最小化,这导致非迭代的二阶重建算法。
发现
在本文中,作者开发了两种不同类型的非迭代二阶重建算法,它们能够从入射波产生的场的部分测量中准确地恢复未知的可穿透障碍物。
原创性/价值
目前的论文是开发完全基于拓扑导数的重建方法的开创性工作,用于解决具有可穿透障碍物的逆散射问题。这里提出的两种算法都能够一步返回多个隐藏和未知障碍物的数量、位置和大小。总之,这些算法的主要特点在于它们是非迭代的,因此对于噪声数据以及独立于初始猜测非常稳健。