We disclose a novel inversion algorithm for electrical impedance tomography in two dimensions, based on a consistent subspace interpretation of the underlying severely ill-posed inverse problem. Whereas conventional output-least-squares algorithms can be regarded as minimizing a specific error norm, solutions are recovered here as the minimizers of a closely related, equality-constrained residual norm problem. The resulting sparse problem formulation defines sets of discrete subspaces, to which admissible solutions necessarily are confined. Unlike for output-least-squares, these subspaces no longer are continuous, but instead will assume a discontinuous form, whereby noise perturbations systematically are restrict in their effects. We formulate an efficient Gauss-Newton iteration for finding a solution to the nonlinear problem, and show that this gives rise to a sequence of sparse matrix problems, for which a substantial better conditioning can be demonstrated than typically observed for output-least-squares. A sparse QR factorization is developed that takes full advantage of the block angular matrix structures.
Truyen, B, Boca, A-C & Hoffmann, R 2007, A subspace-based inversion algorithm for Electrical Impedance Tomography. in P Cristea & R Tuducea (eds), Proceedings NSIP 2007, IEEE-EURASIP International Workshop on Nonlinear Signal and Image Processing. IEEE-EURASIP, Bucharest, Romania, NSIP 2007 International Workshop on Nonlinear Signal and Image Processing, Bucharest, Romania, 10/09/17.
Truyen, B., Boca, A.-C., & Hoffmann, R. (2007). A subspace-based inversion algorithm for Electrical Impedance Tomography. In P. Cristea, & R. Tuducea (Eds.), Proceedings NSIP 2007, IEEE-EURASIP International Workshop on Nonlinear Signal and Image Processing IEEE-EURASIP.
@inproceedings{0fe869fbfce242d49b0ccce5cb75bfe1,
title = "A subspace-based inversion algorithm for Electrical Impedance Tomography",
abstract = "We disclose a novel inversion algorithm for electrical impedance tomography in two dimensions, based on a consistent subspace interpretation of the underlying severely ill-posed inverse problem. Whereas conventional output-least-squares algorithms can be regarded as minimizing a specific error norm, solutions are recovered here as the minimizers of a closely related, equality-constrained residual norm problem. The resulting sparse problem formulation defines sets of discrete subspaces, to which admissible solutions necessarily are confined. Unlike for output-least-squares, these subspaces no longer are continuous, but instead will assume a discontinuous form, whereby noise perturbations systematically are restrict in their effects. We formulate an efficient Gauss-Newton iteration for finding a solution to the nonlinear problem, and show that this gives rise to a sequence of sparse matrix problems, for which a substantial better conditioning can be demonstrated than typically observed for output-least-squares. A sparse QR factorization is developed that takes full advantage of the block angular matrix structures.",
keywords = "Electrical Impedance Tomography, output-least-squares, sparse problems, Gauss-Newton iteration",
author = "Bart Truyen and Ana-Cristina Boca and Ronny Hoffmann",
year = "2007",
month = sep,
day = "10",
language = "English",
editor = "Paul Cristea and Rodica Tuducea",
booktitle = "Proceedings NSIP 2007, IEEE-EURASIP International Workshop on Nonlinear Signal and Image Processing",
publisher = "IEEE-EURASIP",
note = "NSIP 2007 International Workshop on Nonlinear Signal and Image Processing, NSIP ; Conference date: 10-09-2017 Through 12-09-2017",
}