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Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigenvectors of the graph Laplacian. One attractive application of ER is to point clouds, i.e. graphs whose…
This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary…
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…
A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…
The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting…
Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…
Radio-Frequency (RF) imaging concerns the digital recreation of the surfaces of scene objects based on the scattered field at distributed receivers. To solve this difficult inverse scattering problems, data-driven methods are often employed…
In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions,…
We calculate effective impedances of infinite $LC$- and $CL$- ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves precise mathematical concepts. These concepts are related…
Multi-frequency Electrical Impedance Tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods…
Which systems are ideal to obtain negative refraction with no absorption? Electromagnetically induced transparency (EIT) is a method to suppress absorption and make a material transparent to a field of a given frequency. Such a system has…
A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on $X$ which is either observed directly or derived from a data set. For an electrical network there are two…
In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…
A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical impedance tomography (EIT) on the boundary to obtain…
Ultrasound images formed by delay-and-sum beamforming are plagued by artifacts that only clear up after compounding many transmissions. Some prior works pose imaging as an inverse problem. This approach can yield high image quality with few…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that…
We study the problem of efficiently approximating the \textit{effective resistance} (ER) on undirected graphs, where ER is a widely used node proximity measure with applications in graph spectral sparsification, multi-class graph…
This paper presents a multi-resolution reconstruction method for Electrical Impedance Tomography (EIT), referred to as MR-EIT, which is capable of operating in both supervised and unsupervised learning modes. MR-EIT integrates an ordered…
Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…