Related papers: An inverse moving point source problem in electrom…
In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…
Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…
We consider inverse problems for the Einstein equation with a time-depending metric on a 4-dimensional globally hyperbolic Lorentzian manifold $(M,g)$. We formulate the concept of active measurements for relativistic models. We do this by…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the…
We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…
Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
In this paper we generalise the results proved in [N. Katzourakis, An $L^\infty$ regularisation strategy to the inverse source identification problem for elliptic equations, SIAM J. Math. Anal. 51:2, 1349-1370 (2019)] by studying the…
This paper introduces a novel numerical method for the inverse problem of electroencephalography(EEG). We pose the inverse EEG problem as an optimal control (OC) problem for Poisson's equation. The optimality conditions lead to a…
We study an inverse initial-data problem for a nonlinear Schr\"odinger equation in which the initial wave field is reconstructed from lateral measurements. Our approach combines a Legendre-polynomial-exponential-time dimensional reduction…
This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…
This paper addresses the problem of recovering the spatial profile of the source in the complex Ginzburg-Landau equation from regional observation data at fixed times. We establish two types of sufficient measurements for the unique…
In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…
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…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…