Level set methods for structural inversion and image reconstruction

Oliver Dorn, Dominique Lesselier

    Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

    Abstract

    In this chapter, an introduction is given into the use of level set techniques for inverse problems and image reconstruction. Several approaches are presented which have been developed and proposed in the literature since the publication of the original (and seminal) paper by F. Santosa in 1996 on this topic. The emphasis of this chapter, however, is not so much on providing an exhaustive overview of all ideas developed so far but on the goal of outlining the general idea of structural inversion by level sets, which means the reconstruction of complicated images with interfaces from indirectly measured data. As case studies, recent results (in 2D) from microwave breast screening, history matching in reservoir engineering, and crack detection are presented in order to demonstrate the general ideas outlined in this chapter on practically relevant and instructive examples. Various references and suggestions for further research are given as well.
    Original languageEnglish
    Title of host publicationHandbook of Mathematical Methods in Imaging
    EditorsOtmar Scherzer
    Place of PublicationNew York
    PublisherSpringer Nature
    Pages471-532
    Number of pages62
    Edition2nd
    ISBN (Electronic)9781493907908
    ISBN (Print)9781493907892
    DOIs
    Publication statusPublished - 2015

    Keywords

    • Algorithmic Reconstruction
    • Mathematical Imaging and Vision
    • Support Vector Machines
    • Variation in Imaging
    • Wave Phenomena

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