A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography

Hamilton, Sarah J.; Reyes, Juan Manuel; Siltanen, Samuli; Zhang, Xiaoqun

doi:10.1137/15m1025992

Cited by 15 publications

(14 citation statements)

References 70 publications

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“…When the coefficients are not known, we noticed that it takes more iterations to approximate their values than to identify the shapes. These values could be obtained, for instance, from a one-step reconstruction [16] and used as a first guess to recover the interfaces more accurately (see also [39] for a hybrid one-step method). The algorithm can be accelerated using more advanced minimization methods and more efficient forward solvers.…”

Section: Discussionmentioning

confidence: 99%

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

Beretta

Micheletti

Perotto

et al. 2018

Journal of Computational Physics

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In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions.

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Section: Discussionmentioning

confidence: 99%

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

Beretta

Micheletti

Perotto

et al. 2018

Journal of Computational Physics

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show abstract

“…This motivates the use of a scattering transform computed from the forward problem for the prior in an annulus outside the disk of the experimental scattering data. This approach differs significantl from the methods based on post-processing D-bar conductivity images [45], [46]. …”

Section: Methodsmentioning

confidence: 99%

“…Is it possible to obtain the scattering data S(k) for a larger radius R 2 ≥ R? While methods based on post-processing D-bar conductivity images have been proposed [29,30], the work of Alsaker and Mueller [10] is the first D-bar method which directly includes spatial a priori information into the nonlinear reconstruction method. This information is used in the the scattering transform and in the D-bar equation with parameters that can be adjusted to control the amount of influence the prior has on the reconstruction.…”

Section: 3mentioning

confidence: 99%

Incorporating a Spatial Prior into Nonlinear D-Bar EIT Imaging for Complex Admittivities

Hamilton

Mueller

Alsaker

2017

IEEE Trans. Med. Imaging

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Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filterin of nonlinear (nonphysical) Fourier transform data specifi to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filte to include higher frequency components in the reconstruction, in particular, features that are known with high confidence This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.

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“…One can also attempt edge detection based on EIT algorithms originally designed for reconstructing the full conductivity distribution. There are two main approaches: sharpening blurred EIT images in data-driven post-processing [40,41], and applying sparsity-promoting inversion methods such as total variation regularization [25,57,80,20,24,83,86,56,29,87]. As of now, the former approach does not have rigorous analysis available.…”

Section: Conductivitymentioning

confidence: 99%

Propagation and recovery of singularities in the inverse conductivity problem

et al. 2018

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The ill-posedness of Calderón's inverse conductivity problem, responsible for the poor spatial resolution of Electrical Impedance Tomography (EIT), has been an impetus for the development of hybrid imaging techniques, which compensate for this lack of resolution by coupling with a second type of physical wave, typically modeled by a hyperbolic PDE. We show in 2D how, using EIT data alone, to use propagation of singularities for complex principal type PDE to efficiently detect interior jumps and other singularities of the conductivity. Analysis of variants of the CGO solutions of Astala and Päivärinta [Ann. Math., 163 (2006)] allows us to exploit a complex principal type geometry underlying the problem and show that the leading term in a Born series is an invertible nonlinear generalized Radon transform of the conductivity. The wave front set of all higher-order terms can be characterized, and, under a prior, some refined descriptions are possible. We present numerics to show that this approach is effective for detecting inclusions within inclusions.Next, for J ∈ J , defineThen, |J| is even, and thus |J c | = |{1, . . . , n} \ J| ≡ n mod 2.We can partition J = J + ∪ J − ∪ J ± , where J + := {i ∈ J : i ∈ J, i − 1 / ∈ J} J − := {i ∈ J : i − 1 ∈ J, i / ∈ J} (7.9) J ± := {i ∈ J : i − 1 ∈ J, i ∈ J}.

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A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography

Cited by 15 publications

References 70 publications

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

Incorporating a Spatial Prior into Nonlinear D-Bar EIT Imaging for Complex Admittivities

Propagation and recovery of singularities in the inverse conductivity problem

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