Related papers: Revisit to the Inverse Exponential Radon Transform
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…
Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…
We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in…
A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing…
Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…
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…
The significance of the broken ray transform (BRT) is due to its occurrence in a number of modalities spanning optical, x-ray, and nuclear imaging. When data are indexed by the scatter location, the BRT is both linear and shift invariant.…
We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms.…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
In 1927 Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on $\bbr^n$. These formulas differ from the original ones by Radon and seem to be forgotten. We generalize Mader's formulas to totally geodesic…
In this paper, we provide a modern synthesis of the classic inverse compositional algorithm for dense image alignment. We first discuss the assumptions made by this well-established technique, and subsequently propose to relax these…
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…
Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of kinetic equations. Relation of probability density on phase space for…
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…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…