A residual minimizing solver for the inverse problem of EIT

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.

Jaar van publicatie:2011

Trefwoorden:Electrical Impedance Tomography, inverse problems, numerical analysis

Toegankelijkheid:Open