High-Order Regularized Regression in Electrical Impedance Tomography

Nicholas Polydorides, Alireza Aghasi, Eric L. Miller

Research output: Contribution to journalArticlepeer-review

Abstract

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, which maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit function which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy; hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm, and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem.

Original languageEnglish
Pages (from-to)912-943
Number of pages32
JournalSiam journal on imaging sciences
Volume5
Issue number3
DOIs
Publication statusPublished - 2012

Keywords

  • impedance tomography transform
  • quadratic regression
  • Newton's method
  • BOUNDARY-VALUE PROBLEM
  • INVERSE PROBLEMS
  • RESISTIVITY INVERSION
  • DC RESISTIVITY
  • UNIQUENESS
  • MODEL

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