Related papers: Inverse medium problems, saddle point formulation

In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary condition. We will assume that the corresponding far--field pattern or Cauchy data is either known or measured. The…

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…

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…

Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…

The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…

Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…

We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…

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…

Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…

A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…

Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…

Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…

We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…

This paper proposes and analyzes an iterative minimization formulation for search- ing index-1 saddle points of an energy function. This formulation differs from other eigenvector-following methods by constructing a new objective function…

This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape…

We develop a novel method for finding bifurcations for nonlinear systems of equations based on directly finding bifurcations through saddle points of extended quotients. The method is applied to find the saddle-node bifurcation point for…

Saddle point problems have been attracting people's attention in recent years. To solve large and sparse saddle point problems, Uzawa type algorithms were proposed. The main contribution of this paper is to present a new Uzawa-exact type…

We introduce a stress/total-pressure formulation for poroelasticity that includes the coupling with steady nonlinear diffusion modified by stress. The nonlinear problem is written in mixed-primal form, coupling a perturbed twofold…