High-Order Regularized Regression in Electrical Impedance Tomography
Author(s)Polydorides, Nick; Adhasi, Alireza; Miller, Eric L.
DownloadPolydorides-2012-High-Order Regularized Regression in Electrical Impedance Tomography.pdf (1.253Mb)
MetadataShow full item record
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.
DepartmentMIT Energy Initiative
SIAM Journal on Imaging Sciences
Society for Industrial and Applied Mathematics
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.
Final published version