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Ronny Hoffmann, Bart Truyen, Jan Cornelis
 

Proceedings ICIAMགྷ, 6th International Congress on Industrial and Applied Mathematics

Contribution To Book Anthology

Abstract 

We present a subspace based, structure preserving solution method for the problem of Electrical Impedance Tomography, where the conductivity inside a simply connected 2-dimensional domain is sought from noisy and incomplete boundary data. Unlike conventional output-least squares algorithms that can be regarded as minimizing a certain error norm, solutions are recovered here as the minimizers of a closely related residual norm problem. An iterative solution scheme is shown to lead to a sequence of sparse matrix subproblems, with conditioning far more favorable than typically observed in output-least squares. We find that these sparse subproblems demonstrate a particular form of displacement structure that can be further elaborated to finally arrive upon an efficient computational implementation. In the first part of this contribution, we introduce the structured problem formulation, outline the algorithmic approach taken, and summarize some of its numerical properties.

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