Related papers: Optimization methods in direct and inverse scatter…
We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…
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…
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
An optimal mesh size of the sampling region can help to reduce computational burden in practical applications. In this work, we investigate optimal choices of mesh sizes for the identifications of medium obstacles from either the far-field…
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…
We propose a conceptually new method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology and other applications. The method is inspired by the theory of…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
The demand for inverse design is increasing as the ability to fabricate sub-10 nm features expands the design space by orders of magnitude. Efficient inverse design benefits from differentiable models of light-structure interaction. While…
This paper concerns the reconstruction of multiple elastic parameters (Lam\'e parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\mathbb{R}^2$. The direct scattering problem is…
In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bending energy is used as a stabilizing term in Tikhonov…
We are concerned with the inverse scattering problems associated with incomplete measurement data. It is a challenging topic of increasing importance in many practical applications. Based on a prototypical working model, we propose a…
We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…
This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, lossy, flat-plane layer in which the mass density…
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…
We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…