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The inverse scattering problem considered in this paper is to reconstruct multiple sound-soft obstacles from one incident wave and its far field pattern. Based on the ideas of the Kirsch–Kress method and the hybrid Newton method, three variant Newton-type methods are developed for reconstructing the shape of multiple obstacles. The proposed hybrid Newton-type methods I and II can choose auxiliary curves adaptively, and do not require them to be contained in the unknown multiple obstacles. The proposed hybrid Newton-type method III is simpler than the hybrid Newton method developed by Kress in terms of computational complexity since it adopts quasi-Newton iterations in numerical reconstructions. Results of numerical examples show that the proposed methods, especially the one with both adaptively choosing auxiliary curves and quasi-Newton iterations, are more efficient and stable for reconstructing multiple obstacles.

Hybrid Newton-type methods for reconstructing sound-soft obstacles from a single far field