Imaging of small penetrable obstacles based on the topological derivative method. Issue 1 (17th June 2021)

• Record Type: Journal Article
• Authors: Fernandez, Lucas; Prakash, Ravi
• Is Part Of: Engineering computations. Volume 39:Issue 1(2022)
• Page Start: 201
• Page End: 231
• Publication Date: 2021-06-17
• Subjects: Inverse scattering problem -- Penetrable obstacles -- Topology optimization -- Topological derivative method -- Noniterative reconstruction algorithm; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-12-2020-0728
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : 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.