Related papers: Bilinear generalized Radon transforms in the plane

We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…

Given two non-negative functions $f$ and $g$ such that the Radon transform of $f$ is pointwise smaller than the Radon transform of $g$, does it follow that the $L^p$-norm of $f$ is smaller than the $L^p$-norm of $g$ for a given $p>0$? We…

In this paper we introduce and study a Bargmann-Radon transform on the real monogenic Bargmann module. This transform is defined as the projection of the real Bargmann module on the closed submodule of monogenic functions spanned by the…

The star transform is a generalized Radon transform mapping a function of two variables to its integrals along "star-shaped" trajectories, which consist of a finite number of rays emanating from a common vertex. Such operators appear in…

In this work, we study a set of generalized Radon transforms over symmetric $m$-tensor fields in $\mathbb{R}^n$. The longitudinal/transversal Radon transform and corresponding weighted integral transforms for symmetric $m$-tensor field are…

We present a unified approach to the study of Radon transforms related to symmetric groups and to general linear groups GL(n,q) regarded as q-analogues of the former. In both cases, we define a sequence of generalized Radon transforms which…

The two-weight inequality for the Hilbert transform is characterized for an arbitrary pair of positive Radon measures $\sigma$ and $w$ on $\mathbb R$. In particular, the possibility of common point masses is allowed, lifting a restriction…

For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…

Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…

In this paper we show that if $\mu$ is a Borel measure in $\mathbb R^{n+1}$ with growth of order $n$, so that the $n$-dimensional Riesz transform $R_\mu$ is bounded in $L^2(\mu)$, and $B\subset\mathbb R^{n+1}$ is a ball with $\mu(B)\approx…

The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…

Let $G\subset \C P^n$ be a linearly convex compact with smooth boundary, $D={\C}P^n\setminus G$, and let $D^* \subset (\C P^n)^*$ be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of…

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…

We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in $\mathbb{R}^n$. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by…

We consider the weighted Radon transforms $R_W$ along hyperplanes in $R^d, \, d \geq 3$, with strictly positive weights $W = W (x, \theta), \, x \in R^d, \, \theta \in S^{d-1}$. We construct an example of such a transform with non-trivial…

We investigate generalized versions of the Iteratively Regularized Landweber Method, initially introduced in [Appl. Math. Optim., 38(1):45-68, 1998], to address linear and nonlinear ill-posed problems. Our approach is inspired by the…

Given an increasing odd homeomorphism $\sigma$ : R $\rightarrow$ R, the two bijective maps h $\sigma$ , v $\sigma$ : R 2 $\rightarrow$ R 2 dened by h $\sigma$ (x, y) = (x + $\sigma$ --1 (y), y) and v $\sigma$ (x, y) = (x, $\sigma$(x) + y).…

The Radon transform Rf of functions f on SO(3) has recently been applied extensively in texture analysis, i.e. the analysis of preferred crystallographic orientation. In practice one has to determine the orientation probability density…

We consider the inverse problem for the $2$-dimensional weighted local Radon transform $R_m[f]$, where $f$ is supported in $y\geq x^2$ and $R_m[f](\xi,\eta)=\int f(x, \xi x + \eta) m(\xi, \eta, x)\,\text{d} x$ is defined near…

We study the symplectic Radon transform from the point of view of the metaplectic representation of the symplectic group and its action on the Lagrangian Grassmannian. We give rigorous proofs in the general setting of multi-dimensional…