Related papers: Stability on the Inverse Random Source Scattering …
In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…
In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of…
We consider the scattering of time-harmonic plane waves by a compactly supported inhomogeneous scattering obstacle governed by the Helmholtz equation. Given far field observations of the scattered fields corresponding to plane wave incident…
We consider inverse problems for the first and half order time fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates.
We deal with the stability issue for the determination of outgoing time-harmonic acoustic waves from their far-field patterns. We are especially interested in keeping as explicit as possible the dependence of our stability estimates on the…
This paper is concerned with an inverse random potential problem for the Schr\"odinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential…
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…
In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
In this paper we study the inverse problem of identifying a source or an initial state in a time-fractional diffusion equation from the knowledge of a single boundary measurement. We derive logarithmic stability estimates for both…
We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in…
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…
This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. Based on a newly…
In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in $\mathbb R^3$. Firstly, to connect the boundary data with the unknown source, we…
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…