2D D-bar reconstructions of human chest and tank data using an improved approximation to the scattering transform

DeAngelo, Michael V.; Mueller, Jennifer L.

doi:10.1088/0967-3334/31/2/008

Cited by 34 publications

(44 citation statements)

References 26 publications

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“…These solutions were introduced in [17], and involve formulating the problem as an elliptic system. Define as a transformation of and a matrix operator by (12) Defining a vector in terms of the solution to (1), one sees that Francini shows in [17] that for sufficiently small, , and , there exists a unique 2 2 matrix for that is a solution to (13) with , and where the asymptotic condition is made precise in [17]. The columns of serve as two such vectors separately satisfying…”

Section: Description Of the Algorithmmentioning

confidence: 99%

“…Splitting the integral over into a sum of integrals over the subsections Using the expansions for and , (27) and (28), respectively, we have where denotes the action of the discretized matrix on the th normalized basis function evaluated at . Define (29) then (30) Following [13] ( 31) i.e., the th entry in the matrix resulting from multiplication of the normalized current pattern matrix and the discretized difference in DN maps . Using the properties of matrix multiplication, (30) can be rewritten as …”

Section: A Computation Of the Cgo Solutionsmentioning

confidence: 99%

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Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D

Hamilton

Mueller

2013

IEEE Trans. Med. Imaging

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Electrical impedance tomography (EIT) is a medical imaging technique in which current is applied on electrodes on the surface of the body, the resulting voltage is measured, and an inverse problem is solved to recover the conductivity and/or permittivity in the interior. Images are then formed from the reconstructed conductivity and permittivity distributions. In the 2-D geometry, EIT is clinically useful for chest imaging. In this work, an implementation of a D-bar method for complex admittivities on a general 2-D domain is presented. In particular, reconstructions are computed on a chest-shaped domain for several realistic phantoms including a simulated pneumothorax, hyperinflation, and pleural effusion. The method demonstrates robustness in the presence of noise. Reconstructions from trigonometric and pairwise current injection patterns are included.

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Section: Description Of the Algorithmmentioning

confidence: 99%

Section: A Computation Of the Cgo Solutionsmentioning

confidence: 99%

Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D

Hamilton

Mueller

2013

IEEE Trans. Med. Imaging

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“…The specific choice of ζ F will certainly affect the solution. For the 2D problem a similar approximation was used in [27,28].…”

Section: The Reconstruction Algorithmsmentioning

confidence: 99%

“…Inserting (26) and (27) in (25) yields a matrix equation for the coefficients W n ,m , . To be explicit, we replace the indices (n, m, ) and (n , m , ) by the single indices i and i given by…”

Section: Numerical Solution Of the Integral Equation (21)mentioning

confidence: 99%

Electrical impedance tomography: 3D reconstructions using scattering transforms

Delbary

Hansen

Knudsen

2012

Applicable Analysis

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In three dimensions the Calderón problem was addressed and solved in theory in the 1980s. The main ingredients in the solution of the problem are complex geometrical optics solutions to the conductivity equation and a (non-physical) scattering transform. The resulting reconstruction algorithm is in principle direct and addresses the full non-linear problem immediately. In this paper a new simplification of the algorithm is suggested. The method is based on solving a boundary integral equation for the complex geometrical optics solutions, and the method is implemented numerically using a Nyström method. Convergence estimates are obtained using hyperinterpolation operators. We compare the method numerically to two other approximations by evaluation on two numerical examples. In addition a moment method for the numerical solution of the forward problem is given.

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“…( can be constructed by using the inner product method through a method similar to adjacent excitation measurement [9][10][11] or by using a linear transformation [12].…”

Section: A the Helmholtz Equationmentioning

confidence: 99%

Direct image reconstruction for electromagnetic tomography by using the factorization method

Cao

Xu³

et al. 2011

2011 IEEE International Conference on Imaging Systems and Techniques

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A factorization method was introduced to electromagnetic tomography (EMT) in this paper. Compared with the traditional methods based on the sensitivity theorem, the proposed method can generate the reconstructed images directly. Neither matrix inversion nor iterations is needed in the reconstruction process. The reconstruction process is simple, as the test function is calculated according to the fundamental solution to the governing equation, i.e. the Helmholtz equation. Simulated data were used to validate the feasibility and effectiveness of the proposed method for EMT.

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2D D-bar reconstructions of human chest and tank data using an improved approximation to the scattering transform

Cited by 34 publications

References 26 publications

Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D

Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D

Electrical impedance tomography: 3D reconstructions using scattering transforms

Direct image reconstruction for electromagnetic tomography by using the factorization method

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