Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

Gehre, Matthias; Kluth, Tobias; Lipponen, Antti; Jin, Bangti; Seppänen, Aku; Kaipio, Jari P.; Maaß, Peter

doi:10.1016/j.cam.2011.09.035

Cited by 83 publications

(80 citation statements)

References 33 publications

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“…In comparison with the BB GPSR in [21], a more sophisticated version of the BB rule was employed in our study. This BB rule was similarly applied to the standard sparsity algorithm presented in "Appendix", according to [22,23,38]. The step length computed by Eq.…”

Section: Barzilai-borwein Gpsrmentioning

confidence: 99%

“…In this work, the PCG is implemented with the aid of the EIDORS software [19] and is regarded as the first benchmark for evaluating the performance of the proposed inverse solver. The second benchmark is the most well-known sparsity algorithm in EIT [22,23,38], which is outlined in "Appendix". For further theoretical details, the reader is referred to [22,23,38].…”

Section: Preconditioned Conjugate Gradient (Pcg) Inverse Solvermentioning

confidence: 99%

“…To best of our knowledge, the most wellknown algorithm for sparsity reconstruction in EIT was proposed in [38] and was then applied to real experiments [22,23]. Although similar to the GPSR, this algorithm follows a gradient-based method which requires solely matrix-vector products, it does not benefit from the splitting scheme in the GPSR.…”

Section: Introductionmentioning

confidence: 97%

“…Although similar to the GPSR, this algorithm follows a gradient-based method which requires solely matrix-vector products, it does not benefit from the splitting scheme in the GPSR. In addition, a direct application of the gradient of the residual leads to numerical instability for this algorithm, even in two-dimensional cases, so a Sobolev smoothing step is applied to the gradient via solving an augmented Dirichlet boundary value problem at each iterate, which increases the computational cost [22,23,38].…”

Section: Introductionmentioning

confidence: 99%

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A fast time-difference inverse solver for 3D EIT with application to lung imaging

Javaherian

Soleimani

Möeller

2016

Med Biol Eng Comput

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A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

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Section: Barzilai-borwein Gpsrmentioning

confidence: 99%

Section: Preconditioned Conjugate Gradient (Pcg) Inverse Solvermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A fast time-difference inverse solver for 3D EIT with application to lung imaging

Javaherian

Soleimani

Möeller

2016

Med Biol Eng Comput

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“…Many of the inverse problems that arise in these fields can mathematically be formulated as Cauchy problems for elliptic partial differential equations; examples include a classical thermostatics problem which consists of recovering the temperature in a given domain when it's distribution and heat flux are known over the accessible region of the boundary [23,5,4,25], electrostatics problem encountered in electric impedance tomography [13,12], corrosion detection [18,17,1], inverse scattering problems [11,22,3]. Cauchy problems for elliptic equations as with many other inverse problems are known to be ill-posed.…”

Section: Introductionmentioning

confidence: 99%

Non-linear inverse geothermal problems

Wokiyi¹

2017

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The inverse geothermal problem consist of estimating the temperature distribution below the earth's surface using temperature and heat-flux measurements on the earth's surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an non-linear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is non-linear. This problem is ill-posed in the sense that it does not satisfy atleast one of Hadamard's definition of well-posedness.We formulated the problem as an ill-posed non-linear operator equation which is defined in terms of solving a well-posed boundary problem. We demonstrate existence of a unique solution to this well-posed problem and give stability estimates in appropriate function spaces. We show that the operator equation is well-defined in appropriate function spaces.Since the problem is ill-posed, regularization is needed to stabilize computations. We demostrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a wellposed problem related to the operator equation. In this study we demostrate that the algorithm works efficiently for 2D calculations but can also be modified to work for 3D calculations.i

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A reconstruction algorithm for electrical impedance tomography based on sparsity regularization

Jin

Khan

Maaß

2011

Numerical Meth Engineering

Self Cite

117

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SUMMARYThis paper develops a novel sparse reconstruction algorithm for the electrical impedance tomography problem of determining a conductivity parameter from boundary measurements. The sparsity of the 'inhomogeneity' with respect to a certain basis is a priori assumed. The proposed approach is motivated by a Tikhonov functional incorporating a sparsity-promoting`1-penalty term, and it allows us to obtain quantitative results when the assumption is valid. A novel iterative algorithm of soft shrinkage type was proposed. Numerical results for several two-dimensional problems with both single and multiple convex and nonconvex inclusions were presented to illustrate the features of the proposed algorithm and were compared with one conventional approach based on smoothness regularization.

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Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

Cited by 83 publications

References 33 publications

A fast time-difference inverse solver for 3D EIT with application to lung imaging

A fast time-difference inverse solver for 3D EIT with application to lung imaging

Non-linear inverse geothermal problems

A reconstruction algorithm for electrical impedance tomography based on sparsity regularization

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