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A residual minimizing solver for the inverse problem of EIT Host Publication: Proc. 12th International Conference in Electrical Impedance Tomography (EIT 2011), May 4-6, 2011, Bath, UK Authors: B. Truyen, L. Dimiccoli and J. Cornelis Publisher: University of Bath, UK Publication Date: May. 2011 Number of Pages: 4
Abstract: Despite their theoretical limitations and numerically often disappointing performance, Output-
Least-Squares (OLS) algorithms retain a dominant role in solving the inverse problem of Electrical
Impedance Tomography. We present a new approach based on a double-constrained variational
formulation of the problem. The method relies on a nonlinear integral transform, which relates
the conductivity in the interior of a closed domain to the dissipated power as computed from the
Cauchy data on the boundary. The kernel of this transform involves the unknown electric potential
field at the target conductivity function, which on the boundary is constrained by the Dirichlet
conditions. A first-order Taylor series approximation, centred at a known prior, leads to a bilinear
residual expression, which is then used to define a Tikhonov regularized misfit measure on the
discrete Lp norm, where p = 1, 2,?. Unlike for the error measure in OLS, the misfit function is
defined over the entire domain, and not restricted to the boundary. What emerges is an iterative
algorithm requiring the solution of a sequence of sparse matrix problems, the structure of which
is retained during the entire calculation. For p = 2 the iteration essentially reduces to a Gauss-
Newton method. To the expense of computing the misfit measure also over the interior of the
domain, the algorithm lends itself particularly well for accelerated implementations, exploiting the
sparse structure demonstrated by the constitutive matrix problems.
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