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A direct three dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering…
Using advanced machine learning techniques, we developed a method for reconstructing precisely the arrival direction and energy of ultra-high-energy cosmic rays from the voltage traces they induced on ground-based radio detector arrays. In…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…
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…
Magneto-conductance in thin wires often exhibits complicated patterns due to the quantum interference of conduction electrons. These patterns reflect microscopic structures in the wires, such as defects or potential distributions. In this…
We consider the inverse problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
The robust Chinese remainder theorem (CRT) has been recently proposed for robustly reconstructing a large nonnegative integer from erroneous remainders. It has found many applications in signal processing, including phase unwrapping and…
Modern computer vision algorithms have brought significant advancement to 3D geometry reconstruction. However, illumination and material reconstruction remain less studied, with current approaches assuming very simplified models for…
The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…
In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…
We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated…
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…
This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination…
The purpose of this paper is to report on recent approaches to reconstruction problems based on analog, or in other words, infinite-dimensional, image and signal models. We describe three main contributions to this problem. First, linear…
Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper [1] is generalized and used to investigate superconducting state of this model. We use the notion of charge quantum number to describe the irreducible…
Proton deflectometry is increasingly used in magnetized high-energy-density plasmas to observe electromagnetic fields. We describe a reconstruction algorithm to recover the electromagnetic fields from proton fluence data in 1-D. The…
In a transparent three-terminal Josephson junction, modeling nonequilibrium transport is numerically challenging, owing to the interplay between multiple Andreev reflection (MAR) thresholds and multipair resonances in the pair current. An…