1,106 research outputs found
EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments
We review developments, issues and challenges in Electrical Impedance
Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT,
Manchester 2003. We focus on the necessity for three dimensional data
collection and reconstruction, efficient solution of the forward problem and
present and future reconstruction algorithms. We also suggest common pitfalls
or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of
EIT, Manchester, UK, 200
Sparsity prior for electrical impedance tomography with partial data
This paper focuses on prior information for improved sparsity reconstruction
in electrical impedance tomography with partial data, i.e. data measured only
on subsets of the boundary. Sparsity is enforced using an norm of the
basis coefficients as the penalty term in a Tikhonov functional, and prior
information is incorporated by applying a spatially distributed regularization
parameter. The resulting optimization problem allows great flexibility with
respect to the choice of measurement boundaries and incorporation of prior
knowledge. The problem is solved using a generalized conditional gradient
method applying soft thresholding. Numerical examples show that the addition of
prior information in the proposed algorithm gives vastly improved
reconstructions even for the partial data problem. The method is in addition
compared to a total variation approach.Comment: 17 pages, 12 figure
An Analysis of Finite Element Approximation in Electrical Impedance Tomography
We present a finite element analysis of electrical impedance tomography for
reconstructing the conductivity distribution from electrode voltage
measurements by means of Tikhonov regularization. Two popular choices of the
penalty term, i.e., -norm smoothness penalty and total variation
seminorm penalty, are considered. A piecewise linear finite element method is
employed for discretizing the forward model, i.e., the complete electrode
model, the conductivity, and the penalty functional. The convergence of the
finite element approximations for the Tikhonov model on both polyhedral and
smooth curved domains is established. This provides rigorous justifications for
the ad hoc discretization procedures in the literature.Comment: 20 page
Comparing D-Bar and Common Regularization-Based Methods for Electrical Impedance Tomography
Objective: To compare D-bar difference reconstruction with regularized linear reconstruction in electrical impedance tomography. Approach: A standard regularized linear approach using a Laplacian penalty and the GREIT method for comparison to the D-bar difference images. Simulated data was generated using a circular phantom with small objects, as well as a \u27Pac-Man\u27 shaped conductivity target. An L-curve method was used for parameter selection in both D-bar and the regularized methods. Main results: We found that the D-bar method had a more position independent point spread function, was less sensitive to errors in electrode position and behaved differently with respect to additive noise than the regularized methods. Significance: The results allow a novel pathway between traditional and D-bar algorithm comparison
High-order regularized regression in Electrical Impedance Tomography
We present a novel approach for the inverse problem in electrical impedance
tomography based on regularized quadratic regression. Our contribution
introduces a new formulation for the forward model in the form of a nonlinear
integral transform, that maps changes in the electrical properties of a domain
to their respective variations in boundary data. Using perturbation theory the
transform is approximated to yield a high-order misfit unction which is then
used to derive a regularized inverse problem. In particular, we consider the
nonlinear problem to second-order accuracy, hence our approximation method
improves upon the local linearization of the forward mapping. The inverse
problem is approached using Newton's iterative algorithm and results from
simulated experiments are presented. With a moderate increase in computational
complexity, the method yields superior results compared to those of regularized
linear regression and can be implemented to address the nonlinear inverse
problem
Detection of breast cancer with electrical impedance mammography
Electrical Impedance Tomography (EIT) is a medical imaging technique that reconstructs internal electrical conductivity distribution of a body from impedance data that is measured on the body surface, and Electrical Impedance Mammography (EIM) is the technique that applies EIT in breast cancer detection. The use of EIM for breast cancer identification is highly desirable because it is a non-invasive and low-cost imaging technology. EIM has the potential in detecting early stage cancer, however there are still challenges that hindering EIM to be provided as a routine health care system. There are three major groups of obstacles. One is the hardware design, which includes the selection of electronic components, electrode-skin contacting methods, etc. Second is theoretical problems such as electrode configurations, image reconstruction and regularization methods. Third is the development of analysis methods and generation of a cancerous tissue database. Research reported in this thesis strives to understand these problems and aims to provide possible solutions to build a clinical EIM system.
The studies are carried out in four parts. First the functionalities of the Sussex Mk4 EIM system have been studied. Sensitivity of the system was investigated to find out the strength and weakness of the system. Then work has been made on image reconstruction and regularization methods in order to enhance the system’s endurance to noise, also to balance the reconstruction conductivity distribution throughout the reconstructed object. Then a novel cancer diagnosis technique was proposed. It was developed based on the electrical property of human breast tissue and the behaviour or systematic noise, to provide repeatable results for each patient. Finally evaluation has been made on previous EIM systems to find out the major problems. Based on sensitivity analysis, an optimal combined electrode configuration has been proposed to improve sensitivity.
The system has been developed and produced meaningful clinical images. The work makes significant contributions to society. This novel cancer diagnosis method has high accuracy for cancer identification. The combined electrode configuration has also provided flexibilities in the designing of current driving and voltage receiving patterns, thus sensitivity of the EIM system can be greatly improved
DICOM for EIT
With EIT starting to be used in routine clinical practice [1], it important that the clinically relevant information is portable between hospital data management systems. DICOM formats are widely used clinically and cover many imaging modalities, though not specifically EIT. We describe how existing DICOM specifications, can be repurposed as an interim solution, and basis from which a consensus EIT DICOM ‘Supplement’ (an extension to the standard) can be writte
Graph- and finite element-based total variation models for the inverse problem in diffuse optical tomography
Total variation (TV) is a powerful regularization method that has been widely
applied in different imaging applications, but is difficult to apply to diffuse
optical tomography (DOT) image reconstruction (inverse problem) due to complex
and unstructured geometries, non-linearity of the data fitting and
regularization terms, and non-differentiability of the regularization term. We
develop several approaches to overcome these difficulties by: i) defining
discrete differential operators for unstructured geometries using both finite
element and graph representations; ii) developing an optimization algorithm
based on the alternating direction method of multipliers (ADMM) for the
non-differentiable and non-linear minimization problem; iii) investigating
isotropic and anisotropic variants of TV regularization, and comparing their
finite element- and graph-based implementations. These approaches are evaluated
on experiments on simulated data and real data acquired from a tissue phantom.
Our results show that both FEM and graph-based TV regularization is able to
accurately reconstruct both sparse and non-sparse distributions without the
over-smoothing effect of Tikhonov regularization and the over-sparsifying
effect of L regularization. The graph representation was found to
out-perform the FEM method for low-resolution meshes, and the FEM method was
found to be more accurate for high-resolution meshes.Comment: 24 pages, 11 figures. Reviced version includes revised figures and
improved clarit
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