High-Order Regularized Regression in Electrical Impedance Tomography
Name
Polydorides-2012-High-Order Regularized Regression in Electrical Impedance Tomography.pdf
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1.25 MB
Format
Adobe PDF
Checksum (MD5)
15a4fa463ca54d2a6a165cf84ff0b487
Author(s)
Polydorides, Nick
Adhasi, Alireza
Miller, Eric L.
Date Issued
August 2012
Journal
SIAM Journal on Imaging Sciences
Publisher
Society for Industrial and Applied Mathematics
Citation
Polydorides, Nick, Alireza Aghasi, and Eric L. Miller. “High-Order Regularized Regression in Electrical Impedance Tomography.” SIAM Journal on Imaging Sciences 5.3 (2012): 912–943. CrossRef. Web. © 2012, Society for Industrial and Applied Mathematics.
Version
Final published version
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.
MIT Department
MIT Energy Initiative
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/11084724x
