Related papers: On the broken ray transform
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…
Inertial waves in fluid regions of planets and stars play an important role in their dynamics and evolution, through energy, heat and angular momentum transport and mixing of chemicals. While inertial wave propagation in flows prescribed by…
The reflections caused by common semi-reflectors, such as glass windows, can impact the performance of computer vision algorithms. State-of-the-art methods can remove reflections on synthetic data and in controlled scenarios. However, they…
In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…
We compute rest-frame reflection spectra and the corresponding energy-dependent linear polarization degree and angle for (un)polarized single-temperature blackbody spectra impinging on a partially ionized constant-density optically thick…
This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures. A fundamental step in any typical iterative inversion method, is the numerical solution of the underlying direct…
In this paper we consider the geodesic X-ray transform with attenuation coefficient as a combination of smooth complex function and 1-form. We show that attenuated X-ray transform applied to the pair of tensors is injective modulo the…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which…
Curving beams are a promising new method for bypassing obstacles in future millimeter-wave to sub-terahertz (sub-THz) networks but lack a general predictive model for their reflections from arbitrary surfaces. We show that, unfortunately,…
The X-ray transform on the plane or on the three-dimensional Euclidean space can be considered as the measurements of CT scanners for normal human tissue. If the human body contains metal regions such as dental implants, stents in blood…
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…
This paper is devoted to a Radon-type transform arising in Photoacoustic Tomography that uses integrating line detectors. We consider two situations: when the line detectors are tangent to the boundary of a cylindrical domain and when the…
Context. The numerical modeling of the generation and transfer of polarized radiation is a key task in solar and stellar physics research and has led to a relevant class of discrete problems that can be reframed as linear systems. In order…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
This is a continuation of two recent publications of the authors about reconstruction procedures for 3-d phaseless inverse scattering problems. The main novelty of this paper is that the Born approximation for the case of the wave-like…
We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded…
Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized versions of them. These transformations help in the…
We present a novel analysis of a Radon transform, $R$, which maps an $L^2$ function of compact support to its integrals over smooth surfaces of revolution with centers on an embedded hypersurface in $\mathbb{R}^n$. Using microlocal…
We consider the imaging of cosmic strings by using Cosmic Microwave Background (CMB) data. Mathematically, we study the inversion of an X-ray transform in Lorentzian geometry, called the light ray transform. The inverse problem is highly…