Related papers: Iterative Direct Sampling Method for Elliptic Inve…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
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…
In this paper, a modification to the Gradient Sampling (GS) method for minimizing nonsmooth nonconvex functions is presented. One drawback in GS method is the need of solving a Quadratic optimization Problem (QP) at each iteration, which is…
A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the…
This paper investigates the inverse scattering problem of recovering a sound-soft obstacle using passive measurements taken from randomly distributed point sources. The randomness introduced by these sources poses significant challenges,…
The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…
In this work, we investigate the diffusive optical tomography (DOT) problem in the case that limited boundary measurements are available. Motivated by the direct sampling method (DSM), we develop a deep direct sampling method (DDSM) to…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) remains challenging. Because physical domains are naturally…
This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…
Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical…
We consider the direct and inverse scattering problem for a penetrable, isotropic obstacle with a second-order Robin boundary condition, which asymptotically models the delamination of the boundary of the scatterer. We develop a direct…
We consider primal-dual mixed finite element methods for the solution of the elliptic Cauchy problem, or other related data assimilation problems. The method has a local conservation property. We derive a priori error estimates using known…
In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data…
This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…
Inverse medium scattering problems arise in many applications, but in practice, the measurement data are often restricted to a limited aperture by physical or experimental constraints. Classical sampling methods, such as MUSIC and the…
This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…
Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…