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

Does electro-sensing fish use the first order polarization tensor for object characterization? object discrimination test

This paper extends the previous works to further explore the role of the first order polarization tensor in electro-sensing by the weakly electric fish specifically for object discrimination and characterization. The first order polarization tensor for few objects used in the considered experiment are calculated and discussed to identify whether there are other evidences to suggest that a weakly electric fish able to recognize the tensor when choosing or rejecting an object. Our findings in this study suggest that all fish during most of the experiments face difficulties to discriminate two objects when their first order polarization tensors are almost similar depending on the types of training given to them

Uniqueness and reconstruction in magnetic resonance-electrical impedance tomography (MR-EIT)

Magnetic resonance-electrical impedance tomography (MR-EIT) was first proposed in 1992. Since then various reconstruction algorithms have been suggested and applied. These algorithms use peripheral voltage measurements and internal current density measurements in different combinations. In this study the problem of MR-EIT is treated as a hyperbolic system of first-order partial differential equations, and three numerical methods are proposed for its solution. This approach is not utilized in any of the algorithms proposed earlier. The numerical solution methods are integration along equipotential surfaces (method of characteristics), integration on a Cartesian grid, and inversion of a system matrix derived by a finite difference formulation. It is shown that if some uniqueness conditions are satisfied, then using at least two injected current patterns, resistivity can be reconstructed apart from a multiplicative constant. This constant can then be identified using a single voltage measurement. The methods proposed are direct, non-iterative, and valid and feasible for 3D reconstructions. They can also be used to easily obtain slice and field-of-view images from a 3D object. 2D simulations are made to illustrate the performance of the algorithms

Regularised GMRES-type Methods for X-Ray Computed Tomography

Slowly converging iterative methods such as Landweber or ART, have long been preferred for reconstructing a tomographic image from a set of CT data. In the recent years, a fast-converging method named CGLS has received attention for reconstructing tomographic data. However, there is a large class of methods that give more reliable solutions, when compared to CGLS. In this paper, we are going to consider the merits of the GMRES-type methods when applied to the CT problem, introduce various strategies, and compare the results with CGLS

Nonuniqueness in diffusion-based optical tomography

A condition on nonuniqueness in optical tomography is stated. The main result applies to steady-state (dc) diffusion-based optical tomography, wherein we demonstrate that simultaneous unique recovery of diffusion and absorption coefficients cannot be achieved. A specific example of two images that give identical dc data is presented. If the refractive index is considered an unknown, then nonuniqueness also occurs in frequency-domain and time-domain optical tomography, if the underlying model of the diffusion approximation is employed

Generation of anisotropic-smoothness regularization filters for EIT

In the inverse conductivity problem, as in any ill-posed inverse problem, regularization techniques are necessary in order to stabilize inversion. A common way to implement regularization in electrical impedance tomography is to use Tikhonov regularization. The inverse problem is formulated as a minimization of two terms: the mismatch of the measurements against the model, and the regularization functional. Most commonly, differential operators are used as regularization functionals, leading to smooth solutions. Whenever the imaged region presents discontinuities in the conductivity distribution, such as interorgan boundaries, the smoothness prior is not consistent with the actual situation. In these cases, the reconstruction is enhanced by relaxing the smoothness constraints in the direction normal to the discontinuity. In this paper, we derive a method for generating Gaussian anisotropic regularization filters. The filters are generated on the basis of the prior structural information, allowing a better reconstruction of conductivity profiles matching these priors. When incorporating prior information into a reconstruction algorithm, the risk is of biasing the inverse solutions toward the assumed distributions. Simulations show that, with a careful selection of the regularization parameters, the reconstruction algorithm is still able to detect conductivities patterns that violate the prior information. A generalized singular-value decomposition analysis of the effects of the anisotropic filters on regularization is presented in the last sections of the paper

The effects of tomographic scans with fewer radiographs on the image reconstruction

Reconstructing a 2D slice or a 3D volume from a set of insufficient tomographic data is a difficult problem, and it is often tackled with analytical reconstruction algorithms. However, these types of methods fall short on delivering a quality image due to the severe artefacts introduced by the insufficiency of the data. The presented work shows the effects of taking tomographic scans with fewer radiographs on the quality of the reconstructed images. The aim here is to show the advantages of using iterative reconstruction methods over analytical methods, which are demonstrated by a quantitative comparison

The effects of fewer projection tomographic scans on the image reconstruction

Reconstructing a 2D slice or a 3D volume from a set of insufficient tomographic data is a difficult problem, and it is often tackled with analytical reconstruction algorithms. However, these types of methods fall short on delivering a quality image due to the severe artefacts introduced by the insufficiency of the data. The presented work shows the effects of taking tomographic scans with fewer radiographs on the quality of the reconstructed images. The aim here is to show the advantages of using iterative reconstruction methods over analytical methods, which are demonstrated by a quantitative comparison