Convergence Analysis of the Harmonic   $\boldsymbol{B_{{z}}}$   Algorithm with Single Injection Current in MREIT

Song, Yizhuang; Sadleir, Rosalind; Liu, Jijun

doi:10.1137/22m1505438

Cited by 2 publications

(16 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the wellposedness of the above equation, an electrode is usually connected to the ground, i.e. impose an extra condition [37,46] u|…”

Section: The Inverse Problem Of Mreitmentioning

confidence: 99%

“…Indeed, such a restriction is reasonable in the sense that the 3-dimensional object is a locally cylindrical subject with a conductivity that keeps unchanged along z-direction, and the injected currents in the electrodes are also z-independent. For this configuration, the corresponding MREIT problem can be formulated entirely in a 2-dimensional model; see [6,[20][21][22]46] for the details.…”

Section: Reconstruction Algorithmsmentioning

confidence: 99%

“…The main advantage of using the equation ( 9) rather than (7) is that the vector J can be exactly recovered from the measured data B z in the 2-dimensional scenario. To be precise, for a twodimensional case, J can be retrieved from the following lemma [46].…”

Section: Reconstruction Algorithmsmentioning

confidence: 99%

“…The solution of the aforementioned iteration scheme converges to the ground truth conductivity in the sense of C 1 . Please see the [46] for more details.…”

Section: A Single Bz Data Based Reconstruction Algorithmmentioning

confidence: 99%

“…Numerical and phantom experiments results show the high performance of this algorithm. [46] provide the convergence theory of the single current harmonic B z algorithm in C 1 space. For one current MREIT, please also refer to [19,26] for isotropic and [29] for anisotropic conductivity reconstruction algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)

Wang,

Song

2024

Inverse Problems

View full text Add to dashboard Cite

Magnetic resonance electrical impedance tomography (MREIT) is a high-resolution imaging modality that aims to reconstruct the objects' conductivity distributions at low frequency using the measurable $z$-th component of the magnetic flux density obtained from an MRI scanner. Traditional reconstruction algorithms in MREIT use two data subject to two linearly independent current densities. However, the temporal resolution of such a MREIT image is relatively low. Recently, a single current MREIT has been proposed to improve the temporal resolution. Even though a series of reconstruction algorithms have been proposed in the last two decades, the theoretical studies of MREIT are still quite limited. This paper presents the stability theorems for two datum and a single data-based isotropic conductivity reconstruction using MREIT. Using the regularity theory of elliptic partial differential equations, we prove that the only instability in the inverse problem of MREIT comes from taking the second-order derivative of the measured data $B_z$, the $z$-th component of the magnetic flux density. To get a stable reconstruction from the noisy $B_z$ data, we note that the edge structure of $\nabla B_z$ reveals the edge features in the unknown conductivity and provides an edge-preserving denoising approach for the $\nabla B_z$ data. We use a modified Shepp-Logan phantom model to validate the proposed theory and the denoising approach.

show abstract

“…For the wellposedness of the above equation, an electrode is usually connected to the ground, i.e. impose an extra condition [37,46] u|…”

Section: The Inverse Problem Of Mreitmentioning

confidence: 99%

Section: Reconstruction Algorithmsmentioning

confidence: 99%

Section: Reconstruction Algorithmsmentioning

confidence: 99%

“…The solution of the aforementioned iteration scheme converges to the ground truth conductivity in the sense of C 1 . Please see the [46] for more details.…”

Section: A Single Bz Data Based Reconstruction Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)

Wang,

Song

2024

Inverse Problems

View full text Add to dashboard Cite

show abstract

On the reconstruction of medium conductivity by integral equation method based on the Levi function

Zhang,

Liu

2024

IPI

Self Cite

View full text Add to dashboard Cite

Consider an inverse problem of recovering the medium conductivity governed by an elliptic system, with partial information of the solution specified in some internal domain as inversion input. We firstly establish the uniqueness of this inverse problem and the conditional stability of Hölder type in internal domain in terms of the analytic extension of the solution. Then by representing the solution of the direct problem with variable coefficient under the Levi function framework, this nonlinear inverse problem is reformulated as solving a linear integral system provided that the boundary value of the conductivity be known. Then this linear system is regularized to deal with the ill-posedness of the function extension, with an efficient numerical realization scheme for seeking the regularizing solution firstly for the density pair and then for the conductivity to be recovered. Numerical implementations are presented to show the validity of the proposed scheme.

show abstract

Convergence Analysis of the Harmonic \(\boldsymbol{B_{{z}}}\) Algorithm with Single Injection Current in MREIT

Cited by 2 publications

References 38 publications

Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)

Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)

On the reconstruction of medium conductivity by integral equation method based on the Levi function

Contact Info

Product

Resources

About