Related papers: Exact inversion of the conical Radon transform wit…
Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these…
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from $\ell^p$ to $\ell^q$…
We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvi\`ere. We also show solenoidal injectivity of the…
We obtain new inversion formulas for the Funk type transforms of two kinds associated to spherical sections by hyperplanes passing through a common point $A$ which lies inside the n-dimensional unit sphere or on the sphere itself.…
Let $\sigma$ be arc-length measure on $S^1\subset \mathbb R^2$ and $\Theta$ denote rotation by an angle $\theta \in (0, \pi]$. Define a model bilinear generalized Radon transform, $$B_{\theta}(f,g)(x)=\int_{S^1} f(x-y)g(x-\Theta y)\,…
We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new…
The tomographic probability distribution on the phase space (cylinder) related to a circle or an interval is introduced. The explicit relations of the tomographic probability densities and the probability densities on the phase space for…
Tomography is a central tool in medical applications, allowing doctors to investigate patients' interior features. The Radon transform (in two dimensions) is commonly used to model the measurement process in parallel-beam CT. Suitable…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
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…
The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special…
We continue to study the problem of modeling of substitution of production factors motivated by the need for computable mathematical models of economics that could be used as a basis in applied developments. This problem has been studied…
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…
This is a continuation of two recent publications of the authors about reconstruction procedures for 3-d phaseless inverse scattering problems. The main novelty of this paper is that the Born approximation for the case of the wave-like…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner…
We present here a set of lecture notes on tomography. The Radon transform and some of its generalizations are considered and their inversion formulae are proved. We will also look from a group-theoretc point of view at the more general…
The Funk-Radon transform, also known as the spherical Radon transform, assigns to a function on the sphere its mean values along all great circles. Since its invention by Paul Funk in 1911, the Funk-Radon transform has been generalized to…
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…
The paper is devoted to interrelation between the zeta distribution and the Radon transform on the space of $n \times m$ real matrices. We present a self-contained proof of the Fourier transform formula for this distribution. Our method…