Related papers: Resistor network approaches to electrical impedanc…
This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized)…
Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global…
This work extends the results of [Garde and Hyv\"onen, Math. Comp. 91:1925-1953] on series reversion for Calder\'on's problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and…
Effective Resistance (ER) is a fundamental tool in various graph learning tasks. In this paper, we address the problem of efficiently approximating ER on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ with $n$ vertices and $m$ edges.…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
In this paper we investigate the problem of identifying conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We…
In power system dynamic simulation, up to 90% of the computational time is devoted to solve the network equations, i.e., a set of linear equations. Traditional approaches are based on sparse LU factorization, which is inherently sequential.…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein…
We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…
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…
Reflectance bounds the frequency spectrum of illumination in the object appearance. In this paper, we introduce the first stochastic inverse rendering method, which recovers the attenuated frequency spectrum of an illumination jointly with…
We study infinite resistor networks perturbed by line defects, in which the resistances are periodically modified along a single line. Using the Sherman-Morrison identity applied to the reciprocal-space representation of the lattice Green's…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
Magnetic resonance imaging (MRI) based electrical properties tomography (EPT) is the quantification of the conductivity and permittivity of different tissues. These electrical properties can be obtained through different reconstruction…
We introduce a framework for analyzing and designing EIS inversion algorithms. Our framework stems from the observation of four features common to well-defined EIS inversion algorithms, namely (1) the representation of unknown…
Unknown electric conductivities of human tissues is a common issue in medical engineering. Electrical impedance tomography (EIT) is an imaging modality that can be used to determine these conductivities in vivo from boundary measurements.…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
The display devices like HDR10 televisions are increasingly prevalent in our daily life for visualizing high dynamic range (HDR) images. But the majority of media images on the internet remain in 8-bit standard dynamic range (SDR) format.…
Objective: To develop, and demonstrate the feasibility of, a novel image reconstruction method for absolute Electrical Impedance Tomography (a-EIT) that pairs deep learning techniques with real-time robust D-bar methods. Approach: A D-bar…