Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography

Hoffmann, Kristoffer; Knudsen, Kim

doi:10.1007/s11220-014-0096-6

Cited by 17 publications

(32 citation statements)

References 27 publications

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“…This can be observed in Figure 1e, where the edges are fairly well seen and the recovered parameter values are very close to the true ones. We also compare our results with the reconstruction in Figure 1f obtained with the Picard algorithm proposed in [20]. We observe a lot of artifacts and a significant loss of contrast in Figure 1f in comparison to the reconstruction shown in Figure 1e, which suggests that our CDII-SR scheme outperforms the Picard scheme.…”

Section: Numerical Experimentsmentioning

confidence: 64%

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

2019

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A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the interior electric field data corresponding to two boundary voltage measurements, where the conductivity and the electric potential are related through an elliptic PDE arising in electrical impedance tomography. Further, the objective functional consists of a L 1 regularization term that promotes sparsity patterns in the conductivity and a Perona-Malik anisotropic diffusion term that enhances the edges to facilitate high contrast and resolution. This framework is motivated by a similar recent approach to solve an inverse problem in acousto-electric tomography. Several numerical experiments and comparison with an existing method demonstrate the effectiveness of the proposed method for superior image reconstructions of a wide-variety of log-conductivity patterns.

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Section: Numerical Experimentsmentioning

confidence: 64%

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

2019

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“…. , L. Using (34) and the fact that the functions u (m,l,q) are bounded below by a positive constant on Ω ′′ , the vector field in (98) equals…”

Section: (93)mentioning

confidence: 99%

Stabilizing inverse problems by internal data. II: non-local internal data and generic linearized uniqueness

Kuchment

Steinhauer

2015

Anal.Math.Phys.

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In the previous paper [42], the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid) imaging modalities could turn extremely unstable techniques, such as optical tomography or electrical impedance tomography, into stable, good-resolution procedures. It was shown that in all cases of interest, the Fréchet derivative of the forward mapping is a pseudo-differential operator with an explicitly computable principal symbol. If one can set up the imaging procedure in such a way that the symbol is elliptic, this would indicate that the problem was stabilized. In the cases when the symbol is not elliptic, the technique suggests how to change the procedure (e.g., by adding extra measurements) to achieve ellipticity.In this article, we consider the situation arising in acousto-optical tomography (also called ultrasound modulated optical tomography), where the internal data available involves the Green's function, and thus depends globally on the unknown parameter(s) of the equation and its solution. It is shown that the technique of [42] can be successfully adopted to this situation as well. A significant part of the article is devoted to results on generic uniqueness for the linearized problem in a variety of situations, including those arising in acousto-electric and quantitative photoacoustic tomography.

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“…The reconstruction of anisotropic diffusion in AET with three and four sets of power density measurements was considered in [37]. In [26], a linearized version of (3) was used to reconstruct σ using a Newton algorithm. In [49], the sensitivity matrix associated with AET is investigated and the relationship between the electric energy density and the conductivity in this framework is discussed, suggesting that AET may provide high resolution images.…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

“…In addition, a sparse reconstruction method was implemented in [1] with applications to hybrid imaging and later the reconstructions were improved using multifrequency data [2]. Most of these previous works deal with linearization methods [4,31,26]. In some of these works, it has also been demonstrated that for a two-dimensional problem, three sets of interior data give good reconstructions [18,31,37].…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

A New Optimization Approach to Sparse Reconstruction of Log-Conductivity in Acousto-Electric Tomography

Roy¹,

Borzì²

2018

SIAM J. Imaging Sci.

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A new optimization approach to sparse reconstruction of log-conductivity in acousto-electric tomography is presented. This approach considers the minimization of a Tikhonov least-squares functional of measured power density together with an L 1-norm penalization of the log-conductivity to promote sparsity and a Perona-Malik functional to enhance edges. This minimization is performed subject to the differential constraint given by two instances of the EIT equation. The resulting infinitedimensional optimization problem is approximated by finite differences and solved efficiently by a proximal scheme. Numerous pointers to existing literature are given to motivate the present framework and results of numerical experiments are presented that demonstrate the many advantages of the new approach.

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Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography

Cited by 17 publications

References 27 publications

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

Stabilizing inverse problems by internal data. II: non-local internal data and generic linearized uniqueness

A New Optimization Approach to Sparse Reconstruction of Log-Conductivity in Acousto-Electric Tomography

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