High-Order Regularized Regression in Electrical Impedance Tomography

• Main Authors: Polydorides, Nick (Contributor), Adhasi, Alireza (Author), Miller, Eric L. (Author)
• Other Authors: MIT Energy Initiative (Contributor)
• Format: Article
• Language: English
• Published: Society for Industrial and Applied Mathematics, 2013-03-13T19:37:22Z.
• Subjects: Article
• Online Access: Get fulltext

 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.