Related papers: The photography transforms and their analytic inve…
Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a…
Fourier transform is applied to annular beams of simplified flat two-level geometry: bright outer ring with a darker core. The pattern of focal beam profile (i.e. far field) is calculated and characterized with respect of its intensity…
A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical…
New simple proofs are given to some elementary approximate and explicit inversion formulas for Riesz potentials. The results are applied to reconstruction of functions from their integrals over Euclidean planes in integral geometry.
Exposure correction is one of the fundamental tasks in image processing and computational photography. While various methods have been proposed, they either fail to produce visually pleasing results, or only work well for limited types of…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
Let $\mathcal R$ denote the generalized Radon transform (GRT), which integrates over a family of $N$-dimensional smooth submanifolds $\mathcal S_{\tilde y}\subset\mathcal U$, $1\le N\le n-1$, where an open set $\mathcal U\subset\mathbb R^n$…
Images of near-field SAR contains spatial-variant sidelobes and clutter, subduing the image quality. Current image restoration methods are only suitable for small observation angle, due to their assumption of 2D spatial-invariant…
We consider the behavior of the photon number integral under inversion, concentrating on euclidean space. The discussion may be framed in terms of an additive differential $I$ which arises under inversions. The quantity $\int \int I$ is an…
An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices…
We study the use of a learned forward operator in the inverse problem of photoacoustic tomography. The Fourier neural operator to approximate the photoacoustic wave propagation is used. Further, the inverse problem is solved using a…
The inversion theorem for the k-plane Radon transform in R^n is often stated for Schwartz functions, and lately for smooth functions on R^n fulfilling that f(x)=O(|x|^{-N}) for some N>n. In this paper it will be shown, that it suffices to…
We develop a systematic approach for resolving the analytic wave front set for a class of integral geometry transforms appearing in various tomography problems. Combined with microlocal analytic continuation, this leads to uniqueness and…
We study the inverse problem of recovering a vector field in $\mathbb{R}^2$ from a set of new generalized $V$-line transforms in three different ways. First, we introduce the longitudinal and transverse $V$-line transforms for vector fields…
The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In…
The object of this study is an integral operator $\mathcal{S}$ which averages functions in the Euclidean upper half-space $\mathbb{R}_{+}^{n}$ over the half-spheres centered on the topological boundary $\partial \mathbb{R}_{+}^{n}$. By…
We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas…
We study the spherical slice transform which assigns to a function on the $n$-dimensional unit sphere the integrals of that function over cross-sections of the sphere by $k$-dimensional affine planes passing through the north pole. These…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
Hand-held light field (LF) cameras have unique advantages in computer vision such as 3D scene reconstruction and depth estimation. However, the related applications are limited by the ultra-small baseline, e.g., leading to the extremely low…