Related papers: Stability properties for a class of inverse proble…

In this paper, we for the first time prove local solvability and stability of the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The proof…

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…

In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded…

Following a recent paper by N. Mandache (Inverse Problems 17 (2001), pp. 1435-1444), we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to many elliptic inverse problems…

In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…

In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…

This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…

In this article we present three robust instability mechanisms for linear and nonlinear inverse problems. All of these are based on strong compression properties (in the sense of singular value or entropy number bounds) which we deduce…

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

Solution of the discretized Lippmann-Schwinger equation in the spatial frequency domain involves the inversion of a linear operator specified by the scattering potential. To regularize this inevitably ill-conditioned problem, we propose a…

Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…

In this paper, we for the first time prove local solvability and stability of an inverse spectral problem for higher-order ($n > 3$) differential operators with distribution coefficients. The inverse problem consists in the recovery of…

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

For linearized Navier-Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over a time interval and velocity field at…

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…

We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We…

We consider the inverse problem of recovering the optical properties of a highly-scattering medium from acousto-optic measurements. Using such measurements, we show that the scattering and absorption coefficients of the radiative transport…

The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements of some displacement fields inside a medium, we show that a stable reconstruction of elastic…