The often disappointing performance of current reconstruction methods used in Electrical Impedance Tomography, can largely be attributed to the manner in which the underlying nonlinear and severely ill-posed parameter estimation problem is mapped for solution. The application of performant iterative solvers has been largely regarded as computational intractable, given the implicit problem formulation and the dimensionality of the inverse operator. Based on the definition of an alternative criterion function, a new solution approach is outlined, in which the original inverse operator is approximated in terms of a limited number of basis functions. Perhaps the most interesting prospect for this new approach, lies in its extension towards a multi-level definition. In this way, the original inverse operator is naturally seen as the limiting case of a series of discrete operators. What emerges is an alternative hierarchical stabilization scheme that promises to improve upon traditional regularization methods, while simultaneously providing convergence to a global solution.
Truyen, B 2001, A new class of approximating inverse solvers for Electrical Impedance Tomography. in Proceedings SIAM Annual Meeting 2001: Minisymposium Detection and Identification of Landmines. Society for Industrial and Applied Mathematics Publications, Philadelphia, PA, pp. 133-133, SIAM Annual Meeting 2001, San Diego, CA, United States, 9/07/01.
Truyen, B. (2001). A new class of approximating inverse solvers for Electrical Impedance Tomography. In Proceedings SIAM Annual Meeting 2001: Minisymposium Detection and Identification of Landmines (pp. 133-133). Society for Industrial and Applied Mathematics Publications.
@inproceedings{bad283a806ba40fd8c9b079057aff0fe,
title = "A new class of approximating inverse solvers for Electrical Impedance Tomography",
abstract = "The often disappointing performance of current reconstruction methods used in Electrical Impedance Tomography, can largely be attributed to the manner in which the underlying nonlinear and severely ill-posed parameter estimation problem is mapped for solution. The application of performant iterative solvers has been largely regarded as computational intractable, given the implicit problem formulation and the dimensionality of the inverse operator. Based on the definition of an alternative criterion function, a new solution approach is outlined, in which the original inverse operator is approximated in terms of a limited number of basis functions. Perhaps the most interesting prospect for this new approach, lies in its extension towards a multi-level definition. In this way, the original inverse operator is naturally seen as the limiting case of a series of discrete operators. What emerges is an alternative hierarchical stabilization scheme that promises to improve upon traditional regularization methods, while simultaneously providing convergence to a global solution.",
keywords = "Electrical Impedance Tomography, basis functions, multi-level definition, hierarchical stabilization, regularization, global solution",
author = "Bart Truyen",
year = "2001",
language = "English",
pages = "133--133",
booktitle = "Proceedings SIAM Annual Meeting 2001",
publisher = "Society for Industrial and Applied Mathematics Publications",
address = "United States",
note = "SIAM Annual Meeting 2001 : Minisymposium Detection and Identification of Landmines ; Conference date: 09-07-2001 Through 13-07-2001",
}