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This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the…
We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous…
A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…
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…
We study the numerical reconstruction problem in acousto-electric tomography (AET) of recovering the conductivity distribution in a bounded domain from multiple interior power density data. The Two-Point-Gradient-$\Theta$ (TPG-$\Theta$) in…
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 paper, we present a discussion on the algorithms design of Electrical Impedance Tomography (EIT) for biomedical applications. Based on the Maxwell differential equations and the derived the finite element(FE) linear equations, we…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…
This text describes a method to simultaneously reconstruct flow states and determine particle properties from Lagrangian particle tracking (LPT) data. LPT is a popular measurement strategy for fluids in which particles in a flow are…
Magneto-acousto-electric tomography (MAET) combines ultrasound with a static magnetic field to infer the electrical conductivity of an object. In this paper, we present a rigorous quasi-static mathematical model for MAET with magnetic field…
This paper aims at mathematically modeling a new multi-physics conductivity imaging system incorporating mechanical vibrations simultaneously applied to an imaging object together with current injections. We perturb the internal…
The aim of electrical impedance tomography is to reconstruct the admittivity distribution inside a physical body from boundary measurements of current and voltage. Due to the severe ill-posedness of the underlying inverse problem, the…
We consider the problem in Electrical Impedance Tomography (EIT) of identifying one or multiple inclusions in a background-conducting body $\Omega\subset\mathbb{R}^2$, from the knowledge of a finite number of electrostatic measurements…
We present the novel Tensorized Discontinuous Isogeometric Analysis (TDIGA) method applied to the discontinuous Galerkin (DG) time-independent 2-D linearized Boltzmann transport equation (LBTE) with higher-order scattering, discretized with…
Reconstructing images from downsampled and noisy measurements, such as MRI and low dose Computed Tomography (CT), is a mathematically ill-posed inverse problem. We propose an easy-to-use reconstruction method based on Expectation…
This paper introduces a method for approximately eliminating the effect that conductivity changes outside the region of interest have in electrical impedance tomography, allowing to form a local reconstruction in the region of interest…
We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…
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…