Related papers: Stability estimates of inverse random source probl…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…
This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…
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.…
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…
Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…
We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non-linearly on a parameter m and operating on a function u. In the…
A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly…
We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional…
In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…
We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the…
In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…
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…
This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…
This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…