Related papers: A learning-based method for solving ill-posed nonl…
Electrical Impedance Tomography (EIT) is a powerful imaging modality widely used in medical diagnostics, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…
Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to…
Patients suffering from pulmonary diseases typically exhibit pathological lung ventilation in terms of homogeneity. Electrical Impedance Tomography (EIT) is a non-invasive imaging method that allows to analyze and quantify the distribution…
Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary…
Electrical impedance tomography (EIT) is a non-invasive imaging method in which an unknown physical body is probed with electric currents applied on the boundary, and the internal conductivity distribution is recovered from the measured…
Electrical Impedance Tomography (EIT) provides a non-invasive, portable imaging modality with significant potential in medical and industrial applications. Despite its advantages, EIT encounters two primary challenges: the ill-posed nature…
Deep learning has been widely employed to solve the Electrical Impedance Tomography (EIT) image reconstruction problem. Most existing physical model-based and learning-based approaches focus on 2D EIT image reconstruction. However, when…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…
Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the surface of the target. Reconstructing the conductivity distribution…
Professor Pierre Sabatier contributed much to the study of inverse problems in theory and practice. Two of these contributions were a focus on theory that actually supports practice, and the identification of well-posed aspects of inverse…
This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…
Electrical Impedance Tomography (EIT) is a promising noninvasive imaging technique that reconstructs the spatial conductivity distribution from boundary voltage measurements. However, it poses a highly nonlinear and ill-posed inverse…
This paper introduces a new approach for solving electrical impedance tomography (EIT) problems using deep neural networks. The mathematical problem of EIT is to invert the electrical conductivity from the Dirichlet-to-Neumann (DtN) map.…
We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…
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…
Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its severe ill-posedness renders direct operator learning with…
The mathematical problem for Electrical Impedance Tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a…
Parallel-beam X-ray computed tomography (CT) and electrical impedance tomography (EIT) are two imaging modalities which stem from completely different underlying physics, and for decades have been thought to have little in common either…