Nonlinear Fourier analysis for discontinuous conductivities: Computational results

JOURNAL OF COMPUTATIONAL PHYSICS

卷:276

Article

关键词: Inverse problem;    Beltrami equation;    Conductivity equation;    Inverse conductivity problem;    Complex geometrical optics solution;    Nonlinear Fourier transform;    Scattering transform;    Electrical impedance tomography;   

DOI  :  10.1016/j.jcp.2014.07.032

来源: Elsevier

【 摘 要 】

Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global uniqueness proofs for Calderon problem exposed in Nachman (1996) [43] and Astala and Paivarinta (2006) [6]: the Astala-Paivarinta theory-based low-pass transport matrix method implemented in Astala et al. (2011) [3] and the shortcut method which considers ingredients of both theories. The latter method is formally similar to the Nachman theory-based regularized EIT reconstruction algorithm studied in Knudsen et al. (2009) [34] and several references from there. New numerical results are presented using parallel computation with size parameters larger than ever, leading mainly to two conclusions as follows. First, both methods can approximate piecewise constant conductivities better and better as the cutoff frequency increases, and there seems to be a Gibbs-like phenomenon producing ringing artifacts. Second, the transport matrix method loses accuracy away from a (freely chosen) pivot point located outside of the object to be studied, whereas the shortcut method produces reconstructions with more uniform quality. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free