Two FFT Subspace-Based Optimization Methods for Electrical Impedance Tomography

Abstract

Abstract-Two numerical methods are proposed to solve the electric impedance tomography (EIT) problem in a domain with arbitrary boundary shape. The first is the new fast Fourier transform subspace-based optimization method (NFFT-SOM). Instead of implementing optimization within the subspace spanned by smaller singular vectors in subspace-based optimization method (SOM), a space spanned by complete Fourier bases is used in the proposed NFFT-SOM. We discuss the advantages and disadvantages of the proposed method through numerical simulations and comparisons with traditional SOM. The second is the low frequency subspace optimized method (LF-SOM), in which we replace the deterministic current and noise subspace in SOM with low frequency current and space spanned by discrete Fourier bases, respectively. We give a detailed analysis of strengths and weaknesses of LF-SOM through comparisons with mentioned SOM and NFFT-SOM in solving EIT problem in a domain with arbitrary boundary shape.

A Review of Algorithms and Hardware Implementations in Electrical Impedance Tomography (Invited)

“…When the electrode positions and current injection/measurement protocol are determined, J can be computed with the finite element method (FEM) [32]. In addition to the above linear approximation solver, another typical solver of the nonlinear function F is as follows [20,36,37], given through Green's Theorem and Method of Moments (MOM):…”