Related papers: A Hybrid Segmentation and D-bar Method for Electri…
Over the last decade or so, reconstruction methods using $\ell_1$ regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The…
Building on the well-known total-variation (TV), this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be…
The aim of this paper is to show the feasibility of the D-bar method for real-time 2-D EIT reconstructions. A fast implementation of the D-bar method for reconstructing conductivity changes on a 2-D chest-shaped domain is described.…
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…
We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of…
High radiation dose in CT scans increases a lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with Total Variation (TV) regularization have been developed to reconstruct CT images…
In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…
Electrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages. As the current-voltage pairs depend nonlinearly on the conductivity, impedance tomography leads…
For electrical impedance tomography (EIT), most practical reconstruction methods are based on linearizing the underlying non-linear inverse problem. Recently, it has been shown that the linearized problem still contains the exact shape…
A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed that is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…
Electrical capacitance tomography (ECT) has been investigated in many fields due to its advantages of being non-invasive and low cost. Sparse algorithms with l1-norm regularization are used to reduce the smoothing effect and obtain sharp…
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…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
Electrical Impedance Tomography (EIT) systems are becoming popular because they present several advantages over competing systems. However, EIT leads to images with very low resolution. Moreover, the nonuniform sampling characteristic of…
The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…
The D-bar method at negative energy is numerically implemented. Using the method we are able to numerically reconstruct potentials and investigate exceptional points at negative energy. Subsequently, applying the method to Diffusive Optical…
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a…