Related papers: Complexity of Radon transforms
Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an…
This note is an attempt to give an answer for the following old I.M. Gelfand's question: why some important problems of integral geometry (e.g., the Radon transform and others) are related to harmonic analysis on groups, but for other quite…
This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical approaches such as wavelets and Radon transforms by…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
This article presents extensions of the Cram{\'e}r-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev…
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
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…
We study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case. These provide a general mechanism to study Falconer-type problems involving $(k+1)$-point configurations in…
We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability…
In this manuscript, we obtain a plane wave decomposition for the delta distribution in superspace, provided that the superdimension is not odd and negative. This decomposition allows for explicit inversion formulas for the super Radon…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…
The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an accurate discretization. To deal with voxelized images and…
This paper is devoted to a Radon-type transform arising in a version of Photoacoustic Tomography that uses integrating circular detectors. We show that the transform can be decomposed into the spherical Radon transform and the…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
In this paper we study a probabilistic framework for Radon partitions, where our points are chosen independently from the $d$-dimensional normal distribution. For every point set we define a corresponding Radon polytope, which encodes all…
Proton radiography is a technique extensively used to resolve magnetic field structures in high energy density plasmas, revealing a whole variety of interesting phenomena such as magnetic reconnection and collisionless shocks found in…