REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM

Kim Knudsen, Matti Lassas, Jennifer Mueller, Samuli Siltanen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    A strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143 (1996)] for the ill-posed inverse conductivity problem is presented. The strategy utilizes truncation of the boundary integral equation and the scattering transform. It is shown that this leads to a bound on the error in the scattering transform and a stable reconstruction of the conductivity; an explicit rate of convergence in appropriate Banach spaces is derived as well. Numerical results are also included, demonstrating the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero. The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics. Also, the procedure is a novel regularized imaging method for electrical impedance tomography.
    Original languageEnglish
    JournalInverse Problems and Imaging
    Volume3
    Issue number4
    Pages (from-to)599-624
    ISSN1930-8337
    DOIs
    Publication statusPublished - 2009

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