Related papers: Shape optimization for piecewise parameter identif…
In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born…
We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…
This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. However, for singular controls and underlying diffusion dynamics…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with…
We consider the inverse obstacle scattering problem of determining both the shape and the "equivalent impedance" from far field measurements at a fixed frequency. In this work, the surface impedance is represented by a second order surface…
The radiation (reaction, Robin) boundary condition for the continuum diffusion equation is widely used in chemical and biological applications to express reactive boundaries. The underlying trajectories of the diffusing particles are…
We formulate the immersed-boundary method (IBM) as an inverse problem. A control variable is introduced on the boundary of a larger domain that encompasses the target domain. The optimal control is the one that minimizes the mismatch…
In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption…
Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…
In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…
We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…
The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse…
A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…
Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…