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Compact coherent x-ray sources have been the focus of extensive research efforts over the past decades. As a result, several novel schemes like optical and nano-undulators for generating x-ray emissions in "table-top" setups are proposed,…
Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D…
The spectral numerical mode-matching (SNMM) method is developed to simulate the 3D layered multi-region structures. The SNMM method is a semi-analytical solver having the properties of dimensionality reduction to reduce computational costs;…
We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e. mass density and elastic Lam\'e parameters) of a weakly scattering medium from full-field data of scattered waves outside…
In this paper we consider the possibility of application of the quantum inverse scattering method for studying the superconformal field theory and it's integrable perturbations. The classical limit of the considered constructions is based…
Design and reconstruction of 2d and 3d photonic structures are usually carried out by forward simulations combined with optimization or intuition. Reconstruction by means of layer-stripping has been applied in seismic processing as well as…
Electrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages. As the current-voltage pairs depend nonlinearly on the conductivity, impedance tomography leads…
Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…
Sparse inversion of gravity data based on $L_1$-norm regularization is discussed. An iteratively reweighted least squares algorithm is used to solve the problem. At each iteration the solution of a linear system of equations and the…
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…
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…
Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
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…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
In this work, we use multi-view aerial images to reconstruct the geometry, lighting, and material of facades using neural signed distance fields (SDFs). Without the requirement of complex equipment, our method only takes simple RGB images…
This article considers the inverse problem of Magnet resonance electrical impedance tomography (MREIT) in two dimensions. A rigorous mathematical framework for this inverse problem as well as the existing Harmonic $B_z$ Algorithm as a…
We propose an iterative algorithm for the minimization of a $\ell_1$-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices…
Periodic surface structures are nowadays standard building blocks of optical devices. If such structures are illuminated by aperiodic time-harmonic incident waves as, e.g., Gaussian beams, the resulting surface scattering problem must be…
Atmospheric lidar observations provide a unique capability to directly observe the vertical column of cloud and aerosol scattering properties. Detector and solar background noise, however, hinder the ability of lidar systems to provide…