Reconstructions of Chest Phantoms by the D-Bar Method for Electrical Impedance Tomography

Isaacson, David; Mueller, Jennifer L.; Newell, J.C.; Siltanen, Samuli

doi:10.1109/tmi.2004.827482

Cited by 175 publications

(238 citation statements)

References 41 publications

Supporting

Mentioning

229

Contrasting

Unclassified

Order By: Relevance

“…These two regions appear as one in these images, although other reconstruction algorithms have resolved two lungs under similar test conditions, as did the D-bar algorithm on the experimental tank data in Isaacson et al 2004. The probable cause for this distortion is modeling the chest by a disc. It is well known that such an approximation can cause artifacts; see Adler et al 1996, Gersing et al 1996, Kolehmainen et al 1997, Kolehmainen et al 2005 …”

Section: Resultsmentioning

confidence: 83%

Imaging cardiac activity by the D-bar method for electrical impedance tomography

et al. 2006

View full text Add to dashboard Cite

A practical D-bar algorithm for reconstructing conductivity changes from EIT data taken on electrodes in a 2D geometry is described. The algorithm is based on the global uniqueness proof of Nachman (1996 Ann. Math. 143 71-96) for the 2D inverse conductivity problem. Results are shown for reconstructions from data collected on electrodes placed around the circumference of a human chest to reconstruct a 2D cross-section of the torso. The images show changes in conductivity during a cardiac cycle.

show abstract

Section: Resultsmentioning

confidence: 83%

Imaging cardiac activity by the D-bar method for electrical impedance tomography

et al. 2006

View full text Add to dashboard Cite

show abstract

“…We remark that the method of [33,134] uses, besides CGO solutions, the ∂ method introduced in one dimension by Beals and Coifman [21] and generalized to several dimensions in [1,22,136,196]. The ∂ method has been used in numerical reconstruction procedures in two dimensions in [93,172] among others. The proof of [11] relies also on construction of CGO solutions for the conductivity equation with L ∞ coefficients and the ∂ method.…”

Section: The Calderón Problem In Two Dimensionsmentioning

confidence: 99%

Inverse problems: seeing the unseen

2014

View full text Add to dashboard Cite

This survey article deals mainly with two inverse problems and the relation between them. The first inverse problem we consider is whether one can determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. This is called electrical impedance tomography and also Calderón's problem since the famous analyst proposed it in the mathematical literature (Calderón in On an inverse boundary value problem. Seminar on numerical analysis and its applications to continuum physics (Rio de Janeiro, 1980), Soc Brasil Mat. Rio de Janeiro, pp. [65][66][67][68][69][70][71][72][73] 1980). The second is on travel time tomography. The question is whether one can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as a geometry problem, the boundary rigidity problem. Can we determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points? These two inverse problems concern visibility, that is whether we can determine the internal properties of a medium by making measurements at the boundary. The last topic of this paper considers the opposite issue: invisibility: Can one make objects invisible to different types of waves, including light?Communicated by Ari Laptev.

show abstract

“…Isaacson et al demonstrated in [IMNS04,IMNS06] that the D-bar method performs well on practical data measured from laboratory phantoms and from human subjects. The mandatory regularization step was provided by low-pass filtering in the nonlinear frequency domain.…”

Section: (B)mentioning

confidence: 99%

“…2009(a): The numerical evidence from practical imaging experiments [IMNS04,IMNS06] inspired a rigorous regularization proof of convergence in the form of (1.4), see [KLMS09]. This gave an answer to (iii) and outlined a method for choosing the regularization parameter as the inverse of the nonlinear cutoff frequency.…”

Section: (B)mentioning

confidence: 99%

Nonlinear Inversion from Partial EIT Data:Computational Experiments

Hamilton¹,

Siltanen²

2014

Inverse Problems and Applications

Self Cite

View full text Add to dashboard Cite

Abstract. Electrical impedance tomography (EIT) is a non-invasive imaging method in which an unknown physical body is probed with electric currents applied on the boundary, and the internal conductivity distribution is recovered from the measured boundary voltage data. The reconstruction task is a nonlinear and ill-posed inverse problem, whose solution calls for special regularized algorithms, such as D-bar methods which are based on complex geometrical optics solutions (CGOs). In many applications of EIT, such as monitoring the heart and lungs of unconscious intensive care patients or locating the focus of an epileptic seizure, data acquisition on the entire boundary of the body is impractical, restricting the boundary area available for EIT measurements. An extension of the D-bar method to the case when data is collected only on a subset of the boundary is studied by computational simulation. The approach is based on solving a boundary integral equation for the traces of the CGOs using localized basis functions (Haar wavelets). The numerical evidence suggests that the D-bar method can be applied to partial-boundary data in dimension two and that the traces of the partial data CGOs approximate the full data CGO solutions on the available portion of the boundary, for the necessary small k frequencies.

show abstract

Reconstructions of Chest Phantoms by the D-Bar Method for Electrical Impedance Tomography

Cited by 175 publications

References 41 publications

Imaging cardiac activity by the D-bar method for electrical impedance tomography

Imaging cardiac activity by the D-bar method for electrical impedance tomography

Inverse problems: seeing the unseen

Nonlinear Inversion from Partial EIT Data:Computational Experiments

Contact Info

Product

Resources

About