Reconstruction of thin electromagnetic inclusions by a level-set method. (English) Zbl 1173.35737

Summary: We consider a technique of electromagnetic imaging (at a single, non-zero frequency) which uses the level-set evolution method for reconstructing a thin inclusion (possibly made of disconnected parts) with either dielectric or magnetic contrast with respect to the embedding homogeneous medium. Emphasis is on the proof of the concept, the scattering problem at hand being so far based on a two-dimensional scalar model. To do so, two level-set functions are employed; the first one describes location and shape, and the other one describes connectivity and length. Speeds of evolution of the level-set functions are calculated via the introduction of Fréchet derivatives of a least-square cost functional. Several numerical experiments on noiseless and noisy data as well illustrate how the proposed method behaves.


35R30 Inverse problems for PDEs
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
78M50 Optimization problems in optics and electromagnetic theory
Full Text: DOI