A D-Bar Algorithm with A Priori Information for 2-Dimensional Electrical Impedance Tomography

Alsaker, Melody; Mueller, Jennifer L.

doi:10.1137/15m1020137

Cited by 41 publications

(55 citation statements)

References 32 publications

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“…A priori information has been used successfully in iterative reconstruction algorithms to enhance image quality (see, for example, [12], [13], [14], [15], [16], [17], [18], [19], [20], [21] for a partial list), and more recently in [22] in the direct 2-D D-bar method for (real-valued) conductivity reconstruction. In this paper, the method of [22] is extended to the 2-D D-bar algorithm for the reconstruction of complex admittivities [23], [24], [25].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the method of [22] is extended to the 2-D D-bar algorithm for the reconstruction of complex admittivities [23], [24], [25]. The reconstruction algorithm for complex admittivities differs from the D-bar algorithm for real-valued conductivities in the construction of the complex geometrical optics (CGO) solutions.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithm is described briefl in Section 2, and the reader is referred to [23], [24], [25] for further detail. In [22] a method of including a priori information in the 2-D D-bar algorithm for real-valued conductivities was proposed and proved to be a nonlinear regularization strategy. It was tested on simulated data on a circular domain.…”

Section: Introductionmentioning

confidence: 99%

“…It was tested on simulated data on a circular domain. The 2-D D-bar algorithm for reconstructing complex admittivities differs from the algorithm in [22] in several ways. First, a 2 × 2 elliptic system of equations must be solved to recover the complex admittivity, and so the scattering transform becomes a scattering matrix, and a system of firs order PDEs in ∂ z and ∂ z̄ arises for the CGO solutions.…”

Section: Introductionmentioning

confidence: 99%

“…First, a 2 × 2 elliptic system of equations must be solved to recover the complex admittivity, and so the scattering transform becomes a scattering matrix, and a system of firs order PDEs in ∂ z and ∂ z̄ arises for the CGO solutions. In contrast to the method in [22], there are, in fact, two sets of CGO solutions to compute (described in SectionII-B). Second, in contrast to [22], determining the admittivity requires an additional computational step beyond evaluation of the CGO solution at complex frequency k = 0, as is the case for the methods based on [31].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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Improved resolution of D‐bar images of ventilation using a Schur complement property and an anatomical atlas

et al. 2022

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Background: Electrical impedance tomography (EIT) is a nonionizing imaging technique for real-time imaging of ventilation of patients with respiratory distress. Cross-sectional dynamic images are formed by reconstructing the conductivity distribution from measured voltage data arising from applied alternating currents on electrodes placed circumferentially around the chest. Since the conductivity of lung tissue depends on air content, blood flow, and the presence of pathology, the dynamic images provide regional information about ventilation, pulsatile perfusion, and abnormalities. However, due to the ill-posedness of the inverse conductivity problem, EIT images have a coarse spatial resolution. One method of improving the resolution is to include prior information in the reconstruction. Purpose: In this work, we propose a technique in which a statistical prior built from an anatomical atlas is used to postprocess EIT reconstructions of human chest data. The effectiveness of the method is demonstrated on data from two patients with cystic fibrosis. Methods: A direct reconstruction algorithm known as the D-bar method was used to compute a two-dimensional reconstruction of the conductivity distribution in the plane of the electrodes. Reconstructions using one step in an iterative (regularized) Newton's method were also computed for comparison. An anatomical atlas consisting of 1589 synthetic EIT images computed from X-ray computed tomography (CT) scans of 74 adult male subjects was computed for use as a statistical prior. The resolution of the D-bar images was then improved by maximizing the conditional probability density function of an image that is consistent with the a priori information and the statistical model. A new method to evaluate the accuracy of the EIT images using CT scans of the imaged patient as ground truth is presented. The novel approach is tested on data from two patients with cystic fibrosis. Results and Conclusions:The D-bar images resulted in better structural similarity index measures (SSIM) and multiscale (MS) SSIM measures for both subjects using the mask or amplitude evaluation approach than the one-step (regularized) Newton's method. Further improvement was achieved using the Schur complement (SC) approach, with MS-SSIM values of 0.718 and 0.682 using SC evaluated with the mask and amplitude approach, respectively, for PatientThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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A review of electrical impedance tomography in lung applications: Theory and algorithms for absolute images

Martins

Sato

Moura

et al. 2019

Annual Reviews in Control

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Electrical Impedance Tomography (EIT) is under fast development, the present paper is a review of some procedures that are contributing to improve spatial resolution and material properties accuracy, admitivitty or impeditivity accuracy. A review of EIT medical applications is presented and they were classified into three broad categories: ARDS patients, obstructive lung diseases and perioperative patients. The use of absolute EIT image may enable the assessment of absolute lung volume, which may significantly improve the clinical acceptance of EIT. The Control Theory, the State Observers more specifically, have a developed theory that can be used for the design and operation of EIT devices. Electrode placement, current injection strategy and electrode electric potential measurements strategy should maximize the number of observable and controllable directions of the state vector space. A non-linear stochastic state observer, the Unscented Kalman Filter, is used directly for the reconstruction of absolute EIT images. Historically, difference images were explored first since they are more stable in the presence of modelling errors. Absolute images require more detailed models of contact impedance, stray capacitance and properly refined finite element mesh where the electric potential gradient is high. Parallelization of the forward *

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A D-Bar Algorithm with A Priori Information for 2-Dimensional Electrical Impedance Tomography

Cited by 41 publications

References 32 publications

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

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

Improved resolution of D‐bar images of ventilation using a Schur complement property and an anatomical atlas

A review of electrical impedance tomography in lung applications: Theory and algorithms for absolute images

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