A direct D-bar method for partial boundary data electrical impedance tomography with a priori information

Alsaker, Melody; Hamilton, Sarah J.; Hauptmann, Andreas

doi:10.3934/ipi.2017020

Cited by 34 publications

(34 citation statements)

References 47 publications

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“…The inclusion of a priori estimates into iterative reconstruction methods has been demonstrated to provide improved spatial resolution in EIT images (see, for example, [4,5,7,10,11,14,15,21,35,36]). More recently, a method for including a priori information into direct D-bar reconstruction methods was proposed in [2] and extended in [17] and [1]. These methods, which have been demonstrated to provide improved spatial resolution in reconstructions of simulated EIT data, begin with an estimated prior conductivity distribution.…”

Section: (Communicated By Matti Lassas)mentioning

confidence: 99%

“…When the true conductivity distribution is unknown, determining useful conductivity values for the prior poses a significant challenge. Various methods have been suggested in [2,17,1], which use either "blind" estimates for conductivity values, or use regional average, max, or min values extracted directly from preliminary D-bar reconstructions. The novel approach proposed here is motivated by our observation that when the scattering prior t pr is a poor match for t, artifacts tend to develop in the resulting reconstructions, as illustrated in Fig.…”

Section: 1mentioning

confidence: 99%

“…We then form a scattering prior t pr from (9). As in [2,17,1], this information is inserted into the D-bar algorithm in two distinct ways, which are described as follows.…”

mentioning

confidence: 99%

“…In [17,1], the computation (12) was accomplished with a slight refinement, in which a thresholding parameter was used to detect blow-up in t(k) for |k| ≤ R 1 , and this unstable scattering data t(k) was further truncated and replaced with values t pr (k).…”

mentioning

confidence: 99%

“…This will be discussed in further detail within this section. In our method, as in [2,17,1], we may control the influence of the prior by adjusting R 2 .…”

mentioning

confidence: 99%

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Use of an optimized spatial prior in D-bar reconstructions of EIT tank data

Alsaker¹,

Mueller²

2018

Inverse Problems &Amp; Imaging

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The aim of this paper is to demonstrate the feasibility of using spatial a priori information in the 2-D D-bar method to improve the spatial resolution of EIT reconstructions of experimentally collected data. The prior consists of imperfectly known information about the spatial locations of inclusions and the assumption that the conductivity is a mollified piecewise constant function. The conductivity values for the prior are constructed using a novel method in which a nonlinear constrained optimization routine is used to select the values for the piecewise constant function that give the best fit to the scattering transform computed from the measured data in a disk. The prior is then included in the high-frequency components of the scattering transform and in the computation of the solution of the D-bar equation, with weights to control the influence of the prior. In addition, a new technique is described for selecting regularization parameters to truncate the measured scattering data, in which complex scattering frequencies for which the values of the scattering transform differ greatly from those in the scattering prior are omitted. The effectiveness of the method is demonstrated on EIT data collected on saline-filled tanks with agar heart and lungs with various added inhomogeneities.

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Section: (Communicated By Matti Lassas)mentioning

confidence: 99%

Section: 1mentioning

confidence: 99%

“…We then form a scattering prior t pr from (9). As in [2,17,1], this information is inserted into the D-bar algorithm in two distinct ways, which are described as follows.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…This will be discussed in further detail within this section. In our method, as in [2,17,1], we may control the influence of the prior by adjusting R 2 .…”

mentioning

confidence: 99%

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Use of an optimized spatial prior in D-bar reconstructions of EIT tank data

Alsaker¹,

Mueller²

2018

Inverse Problems &Amp; 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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