A general scheme for constructing inversion algorithms for cone beam CT.
A mixed norm estimate for the X-ray tranform.
A support theorem for the complex Radon transform.
An X-ray transform estimate in Rn.
We prove an x-ray estimate in general dimension which is a stronger version of Wolff's Kakeya estimate [12]. This generalizes the estimate in [13], which dealt with the n = 3 case.
Back-scattering and nonlinear Radon transformation
Characterization of the range of the Radon transform on homogeneous trees.
Connection between the harmonic analysis on the sphere and the harmonic analysis on the one-sheeted hyperboloid: an analytic continuation viewpoint - I.
Connection between the harmonic analysis on the sphere and the harmonic analysis on the one-sheeted hyperboloid: an analytic continuation viewpoint - II.
Connection between the harmonic analysis on the sphere and the harmonic analysis on the one-sheeted hyperboloid: an analytic continuation viewpoint - III.
Directional operators and mixed norms.
We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calderón and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting questions remain unanswered.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential...
Discrete analogues of singular and maximal Radon transforms.
Estimation of anisotropic gaussian fields through Radon transform
We estimate the anisotropic index of an anisotropic fractional brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional brownian field and prove that these processes admit...
Estimation of anisotropic Gaussian fields through Radon transform
We estimate the anisotropic index of an anisotropic fractional Brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional Brownian field and prove that these processes...
Examples of Non-Uniqueness for the Combinatorial Radon Transform Modulo the Symmetric Group.
Extension of separately analytic functions and applications to range characterization of the exponential Radon transform
We consider the problem of characterizing the range of the exponential Radon transform. The proof uses extension properties of separately analytic functions, and we prove a new theorem about extending such functions.
Extension sets for real analytic functions and applications to Radon transforms.
Geometry of stationary sets for the wave equation in . The case of finitely supported initial data: An announcement.
Harmonic interpolation based on Radon projections along the sides of regular polygons
Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented.
Injectivité de la transformation de Radon sur les grassmanniennes
Injectivity Sets for Spherical Means on the Heisenberg Group.