STRUCTURAL STABILITY IN A MINIMIZATION PROBLEM AND APPLICATIONS TO CONDUCTIVITY IMAGING

    Authors

    M. Z. Nashed;A. Tamasan

    Comments

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    Abbreviated Journal Title

    Inverse Probl. Imaging

    Keywords

    Non-smooth optimization; bounded variation; degenerate elliptic; equations; regularization; conductivity imaging; ELECTRICAL-IMPEDANCE TOMOGRAPHY; MAGNETIC-RESONANCE; RECONSTRUCTION; MREIT; Mathematics, Applied; Physics, Mathematical

    Abstract

    We consider the problem of minimizing the functional integral(Omega)a vertical bar del u vertical bar dx, with u in some appropriate Banach space and prescribed trace f on the boundary. For a is an element of L(2) (Omega) and u in the sample space H(1)(Omega), this problem appeared recently in imaging the electrical conductivity of a body when some interior data are available. When a is an element of C(Omega) boolean AND L(infinity)(Omega), the functional has a natural interpretation, which suggests that one should consider the minimization problem in the sample space BV(Omega). We show the stability of the minimum value with respect to a, in a neighborhood of a particular coe ffi cient. In both cases the method of proof provides some convergent minimizing procedures. R We also consider the minimization problem for the non- degenerate functional integral(Omega) a max{vertical bar del u vertical bar delta}dx, for some delta > 0, and prove a stability result. Again, the method of proof constructs a minimizing sequence and we identify su ffi cient conditions for convergence. We apply the last result to the conductivity problem and show that, under an a posteriori smoothness condition, the method recovers the unknown conductivity.

    Journal Title

    Inverse Problems and Imaging

    Volume

    5

    Issue/Number

    1

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    219

    Last Page

    236

    WOS Identifier

    WOS:000287735000012

    ISSN

    1930-8337

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