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Luca Dimiccoli, Bart Truyen, Jan Cornelis
 

Proceedings International Workshop Numerical Linear Algebra in Signals and Systems

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 favourable 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 second part of this contribution, we investigate in more detail the different sparsity patterns deriving from the problem formulation, and illustrate how these connect with the original concept of displacement structure.

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