Related papers: Global Convergence and Uniqueness for an Inverse P…
We consider fractional diffusion-wave equations with source term which is represented in a form of a product of a temporal function and a spatial function. We prove the uniqueness for inveres source problem of determining spatially varying…
The uniqueness of the $L_p$-Minkowski problem has been a long standing problem in convex geometry. In the groundbreaking paper by Brendle-Choi-Daskalopoulos (Acta Math, {\bf219}, 2017), a full uniqueness result was shown for the subcritical…
This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the unique recovery of sound-soft obstacles with a smooth boundary…
For fixed positive integer $n$, $p\in[0,1]$, $a\in(0,1)$, we prove that if a function $g:\mathbb{S}^{n-1}\to \mathbb{R}$ is sufficiently close to 1, in the $C^a$ sense, then there exists a unique convex body $K$ whose $L_p$ curvature…
Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…
We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many…
By developing the d-bar approach to global "inverse scattering" at zero energy we give a principal effectivization of the global reconstruction method for the Gel'fand-Calderon inverse boundary value problem in three dimensions. This work…
In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. The most important…
The initial-value problem for cylindrical gravitational waves is studied through the development of the inverse scattering method scheme. The inverse scattering transform in this case can be viewed as a transformation of the Cauchy data to…
The time dependent experimental data are always collected at discrete grids with respect to the time t. The step size h of such a grid is always separated from zero by a certain positive number. The same is true for all computations, which…
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…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We…
The inverse problem of finding the refraction coefficient of a shallow ocean from the observation of the extra Cauchy data for the acoustic field at the surface of the ocean is studied. Uniqueness theorem is proved and a reconstruction…
In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…
Inverse classification is the process of perturbing an instance in a meaningful way such that it is more likely to conform to a specific class. Historical methods that address such a problem are often framed to leverage only a single…
The conformal formulation of the Einstein constraint equations has been studied intensively since the modern version of the conformal method was first pub- lished in the early 1970s. Proofs of existence and uniqueness of solutions were…