Related papers: A data-assisted two-stage method for the inverse r…

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…

This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…

We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In the first step, an approximate direct sampling method is developed to obtain the locations of the…

We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…

The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the…

In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…

The Kaczmarz method is successfully used for solving discretizations of linear inverse problems, especially in computed tomography where it is known as ART. Practitioners often observe and appreciate its fast convergence in the first few…

The classical Kaczmarz iteration and its randomized variants are popular tools for fast inversion of linear overdetermined systems. This method extends naturally to the setting of the phase retrieval problem via substituting at each…

One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…

A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…

This paper tackles the data completion problem related to the Helmholtz equation. The goal is to identify unknown boundary conditions on parts of the boundary that cannot be accessed directly, by making use of measurements collected from…

It is well-known that in inverse problems, end-to-end trained networks overfit the degradation model seen in the training set, i.e., they do not generalize to other types of degradations well. Recently, an approach to first map images…

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…

We consider a two-stage procedure (TSP) for estimating an inverse regression function at a given point, where isotonic regression is used at stage one to obtain an initial estimate and a local linear approximation in the vicinity of this…

In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In…

This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…