Related papers: Direct Method for Calculating the Inverse Radon Tr…
This paper extends the Radon transform, a classical image processing tool for fast tomography and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform (PDRT), called quantum Radon transform (QRT), is…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in…
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 inversion problem for rational B\'ezier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct an inversion formula but finding the corresponding value…
This paper describes a coplanar non invasive non destructive capacitive imaging device. We first introduce a mathematical model for its output, and discuss some of its theoretical capabilities. We show that the data obtained from this…
Currently, theory of ray transforms of vector and tensor fields is well developed, but the Radon transforms of such fields have not been fully analyzed. We thus consider linearly weighted and unweighted longitudinal and transversal Radon…
The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon transform arises in several contemporary imaging techniques, as…
A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
This work extends the applicability of our recent convexification-based algorithm for constructing images of the dielectric constant of buried or occluded target. We are orientated towards the detection of explosive-like targets such as…
Common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial…
The principal aim of the present paper is to develop the theory of Gelfand pairs on the symmetric group in order to define and study the horocyclic Radon transform on this group. We also find a simple inversion formula for the Radon…
Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and…
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…
We consider a real manifold of dimension 3 or 4 with Minkovsky metric, and with a connection for a trivial GL(n,C) bundle over that manifold. To each light ray on the manifold we assign the data of paralel transport along that light ray. It…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
In this paper the generalized Radon transform over level hypersurfaces of CES-functions of measures supported in positive orthant is studied. A characterization of the generalized Radon transform of nonnegative measures is found. Explicit…
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…