Related papers: Inverse source problems in transport via attenuate…
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the…
This paper is about perfectly electrically conducting structures designed to produce negligible scattered power when exposed to a time-harmonic plane electromagnetic wave. The structures feature cavities capable of concealing objects.…
This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. We show…
The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear…
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…
We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models, in the high-frequency limit. In particular, we evaluate the asymptotic…
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…
Popularized by their strong image generation performance, diffusion and related methods for generative modeling have found widespread success in visual media applications. In particular, diffusion methods have enabled new approaches to data…
Study of a simple single-trace transmission example shows how an extended source formulation of full-waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via…
Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…
In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…
Context. The numerical modeling of the generation and transfer of polarized radiation is a key task in solar and stellar physics research and has led to a relevant class of discrete problems that can be reframed as linear systems. In order…
Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…
We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by…
This paper concerns the reconstruction of an anisotropic diffusion tensor $\gamma=(\gamma_{ij})_{1\leq i,j\leq 2}$ from knowledge of internal functionals of the form $\gamma\nabla u_i\cdot\nabla u_j$ with $u_i$ for $1\leq i\leq I$ solutions…
The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…
We have studied the weakly non-linear quantum transport properties of a two-dimensional quantum wire which can be solved exactly. The non-linear transport coefficients have been calculated and interesting physical properties revealed. In…