Related papers: A globally convergent numerical method for a 1-d i…
This paper studies the reconstruction of Stekloff eigenvalues and the index of refraction of an inhomogeneous medium from Cauchy data. The inverse spectrum problem to reconstruct Stekloff eigenvalues is investigated using a new integral…
This paper proposes a neural network approach for solving two classical problems in the two-dimensional inverse wave scattering: far field pattern problem and seismic imaging. The mathematical problem of inverse wave scattering is to…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
The inverse-scattering problem of an inhomogeneous material has been of interest for many years, and was generally addressed with various optimization techniques. In this paper, we suggest an optimization-free method for solving the…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…
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…
The contrast source inversion (CSI) method and the subspace-based optimization method (SOM) are first proposed in 1997 and 2009, respectively, and subsequently modified. The two methods and their variants share several properties and thus…
Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish…
The Carleman embedding method is a widely used technique for linearizing a system of nonlinear differential equations, but fails to converge in regions where there are multiple fixed points. We propose and test three different versions of a…
This study presents an experimental investigation of the recently established generalized linear sampling method (GLSM) for non-destructive evaluation of damage in elastic materials. To this end, ultrasonic shear waves are generated in a…
We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the…
We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a…