Related papers: Solving the Inverse Source Problem in Femtoscopy w…
In high-energy collisions, we can obtain information about the source function by measuring the two-particle Bose-Einstein correlation function and considering its relationship with the phase-space density of the particle-emitting source.…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
One can access the space-time development of a heavy-ion reaction directly by imaging the source function from two particle correlation functions. In the case of like-charged pions, this imaging can be recast as a Fourier inversion problem.…
Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are…
This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…
We consider the statistical inverse problem of recovering a function $f: M \to \mathbb R$, where $M$ is a smooth compact Riemannian manifold with boundary, from measurements of general $X$-ray transforms $I_a(f)$ of $f$, corrupted by…
We consider a statistical inverse learning problem, where the task is to estimate a function $f$ based on noisy point evaluations of $Af$, where $A$ is a linear operator. The function $Af$ is evaluated at i.i.d. random design points $u_n$,…
The aim of this article is to present a hybrid finite element/finite difference method which is used for reconstructions of electromagnetic properties within a realistic breast phantom. This is done by studying the mentioned properties'…
This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…
In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by…
This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…
Microscopic methods and tools to describe nuclear dynamics have considerably been improved in the past few years. They are based on the time-dependent Hartree-Fock (TDHF) theory and its extensions to include pairing correlations and quantum…
Dealing with the inverse source problem for the scalar wave equation, we have shown recently that we can reconstruct the space-time dependent source function from the measurement of the wave, collected at a single point $x$ for a large…
Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…
In this paper, we consider the prediction of the helium concentrations as function of a spatially variable source term perturbed by fractional Brownian motion. For the direct problem, we show that it is well-posed and has a unique mild…
In this study a simple toy model solution to the missing gravity problem on galactic scales is reverse engineered from galactic data via imposing broad assumptions. It is shown that the toy model solution can be written in terms of baryonic…
We discuss imaging sources from low relative-velocity correlations in heavy-ion reactions. When the correlation is dominated by interference, we can obtain the images by Fourier transforming the correlation function. In the general case, we…
Three-pion interferometry is investigated for new information on the space-time structure of the pion source created in ultra-relativistic heavy-ion collisions. The two- and three-pion correlations are numerically computed for incoherent…