Related papers: On iterative reconstruction in the nonlinearized p…
Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
A geometric view of the polarimetric properties of a nondepolarizing medium is presented by means of a pair of vectors in the Poincar\'e sphere. An alternative representation constituted by a set of vectors contained in the equatorial plane…
The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…
The missing phase problem in X-ray crystallography is commonly solved using the technique of molecular replacement, which borrows phases from a previously solved homologous structure, and appends them to the measured Fourier magnitudes of…
This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…
The possibility of integration of two important categories of optical components, i.e., circular polarizer and lens, into a thin plasmonic metasurface is examined. After exploring general theoretical formulation, optimal designs to realize…
This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem…
We predict nonlinear optical polarization rotation in two dimensional massless Dirac systems including graphene and 8-$Pmmn$ borophene. When illuminated, a continuous wave optical field leads to a nonlinear steady state of photo-excited…
We derive an explicit inversion algorithm for the spherical Radon transform in odd dimensions with partial radial data. We prove that the reconstruction of the unknown function can be reduced to solving ordinary differential equations,…
We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each…
A direct three dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering…
We present here a general approach to treat reflection and refraction of light of arbitrary polarization from single axis anisotropic plates. We show that reflection from interface inside the anisotropic medium is accompanied by beam…
Anisotropic Non-Linear Diffusion is a powerful image processing technique, which allows to simultaneously remove the noise and enhance sharp features in two or three dimensional images. Anisotropic Diffusion is understood here in the sense…
In this work we consider the inverse problem of reconstructing the optical properties of a layered medium from an elastography measurement where optical coherence tomography is used as the imaging method. We hereby model the sample as a…
Within the paradigm of metamaterials and metasurfaces, electromagnetic properties of composite materials can be engineered by shaping or modulating their constituents, so-called meta-atoms. Synthesis and analysis of complex-shape meta-atoms…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…
Line scattering polarization can be strongly affected by Rayleigh scattering by neutral hydrogen and Thompson scattering by free electrons. Often a continuum depolarization results, but the Doppler redistribution produced by the continuum…