Related papers: Iterative Direct Sampling Method for Elliptic Inve…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
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…
In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here we will propose and…
In the recent developments of regularization theory for inverse and ill-posed problems, a variational quasi-reversibility (QR) method has been designed to solve a class of time-reversed quasi-linear parabolic problems. Known as a PDE-based…
This paper considers an inverse shape problem for recovering an unknown clamped obstacle in two dimensions from far--field measurements generated by a single incident wave or just a few incident waves for the biharmonic (flexural) wave…
A direct sampling method (DSM) is designed herein for a real-time detection of small anomalies from scattering parameters measured by a small number of dipole antennas. Applicability of the DSM is theoretically demonstrated by proving that…
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…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…
Developments in numerical methods for problems governed by nonlinear partial differential equations underpin simulations with sound arguments in diverse areas of science and engineering. In this paper, we explore the regularization method…
We have developed a new technique called Direct Shear Mapping (DSM) to measure gravitational lensing shear directly from observations of a single background source. The technique assumes the velocity map of an un-lensed, stably-rotating…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
In this paper, we investigate the Cauchy problem for both linear and semi-linear elliptic equations. In general, the equations have the form \[ \frac{\partial^{2}}{\partial…
This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface…