Related papers: The Broken Ray Transform: Additional Properties an…
Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…
We study the integral transform over a general family of broken rays in $\mathbb{R}^2$. It is natural for broken rays to have conjugate points, for example, when they are reflected from a curved boundary. If there are conjugate points, we…
The windowed ray transform is a natural generalization of the "Analytic-Signal Transform" which is developed to extend arbitrary functions from $\RR^n$ to $\CC^n$. We present several inversion formulas here.
An inverse scattering problem for SAR data in application to through-the-wall imaging is addressed. In contrast with the conventional algorithms of SAR imaging, that work with the linearized mathematical model based on the Born…
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…
This paper presents the rigorous mathematical construction and foundational properties of the Divergence-Free Radiant Transform (DFRT), a spectral transform specifically designed for divergence-free vector fields, with applications in…
Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve…
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…
X-ray scattering patterns from emerging single particle experiments have commonly many missing or contaminated pixels. This complicates different analyses including projections on Fourier or other basis functions (for noise suppression,…
The problem of errors, arising due to finite BPM resolution, in the difference orbit parameters, which are found as a least squares fit to the BPM data, is one of the standard and important problems of accelerator physics. Even so for the…
In optical diffraction tomography (ODT), the three-dimensional scattering potential of a microscopic object rotating around its center is recovered by a series of illuminations with coherent light. Reconstruction algorithms such as the…
Ray-tracing (RT) has become central to site-specific electromagnetic propagation modeling in dynamic complex environments. Yet its computational burden grows sharply as high-fidelity digital twins of these environments scale to millions of…
One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse…
Some inverse problems in high-energy physics, neutron diffraction and NMR spectroscopy are discussed. To solve them, the Fourier integrated transformation method and the Maximum Entropy Technique (MENT) were used. The integrated images of…
We study the inversion of the conical Radon which integrates a function in three-dimensional space from integrals over circular cones. The conical Radon recently got significant attention due to its relevance in various imaging applications…
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
The characteristics of backward diffraction radiation (BDR), i.e. radiation of the charged particle passing through a slit in the tilted screen, has been considered. The technique for non-destructive beam diagnostics based on the…
Monte Carlo radiative transfer (MCRT) simulations are a powerful tool for determining the appearance of astrophysical objects, analyzing the prevalent physical conditions within them, and inferring their properties on the basis of real…
We propose a new algorithm to compute the X-ray transform of an image represented by unit (pixel/voxel) basis functions. The fundamental issue is equivalently calculating the intersection lengths of the ray with associated units. For any…