Related papers: An Inverse Problem for Localization Operators
We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving existence and…
This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
In this paper, we study the performance of Full Waveform Inversion (FWI) from time-harmonic Cauchy data via conditional well-posedness driven iterative regularization. The Cauchy data can be obtained with dual sensors measuring the pressure…
A version of the so-called "convexification" numerical method for a coefficient inverse scattering problem for the 3D Hemholtz equation is developed analytically and tested numerically. Backscattering data are used, which result from a…
We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…
We consider the localization of eigenfunctions for the operator $L=-\mbox{div} A \nabla + V$ on a Lipschitz domain $\Omega$ and, more generally, on manifolds with and without boundary. In earlier work, two authors of the present paper…
We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
The paper investigates the sensitivity of the inverse problem of recovering the velocity field in a bounded domain from the boundary dynamic Dirichlet-to-Neumann map (DDtN) for the wave equation. Three main results are obtained: (1)…
Generalized smooth functions are a possible formalization of the original historical approach followed by Cauchy, Poisson, Kirchhoff, Helmholtz, Kelvin, Heaviside, and Dirac to deal with generalized functions. They are set-theoretical…
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…
We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the…
A simple sufficient condition on curved end of a straight cylinder is found that provides a localization of the principal eigenfunction of the mixed boundary value for the Laplace operator with the Dirichlet conditions on the lateral side.…
This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…