In this paper we develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross-section of a body using almost completely local data which significantly reduces the amount of exposure and computations in X-ray tom...

We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S nor to S. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms fr...

In this paper, skew estimation and correction method for document image has been presented. Image of text document can be acquired via camera or other type of machines which cause sometime a skew angle (alignment) on its horizontal direction. To find skew angle of document image, the Radon transform method is used here. The skew angle used in database within the range of ±90o w.r.t x-axis. Kew ...

New fast algorithms for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. Algorithms are based on new version of General Ray (GR) method which consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE). The class of the PDE includes the L...

We present a novel approach to parameterised curve detection. The method is based on the generalised Radon transform, which is traditionally applied to a 2D edge/line map. The novelty of our method is the mapping of the original 2D image to a 3D orientation space, which then forms the input for the Radon transform. The orientation space representation offers important advantages. It can represe...

We propose a stable and fast reconstruction technique for parallel-beam (PB) tomographic X-ray imaging, relying on the discrete pseudo-polar (PP) Radon transform. Our main contribution is a resampling method, based on modern sampling theory, that transforms the acquired PB measurements to a PP grid. The resampling process is both fast and accurate, and in addition, simultaneously denoises the m...

This paper presents a novel optical system for the realization of the Radon transform in a single frame. The optical system is simple, fast and accurate and consists of a 4F system, where in the 2F plane a vortex like optical element is placed. This optical element performs the rotation of the object, which replaces the need for mechanically rotating it, as is done in other common optical reali...

When for example a blood flow is measured by ultrasound Doppler tomography, part of the received data can be modelled as the Radon transform of the region of reflecting particles. The reconstruction problem thus consists of determining a homogeneous object (that is to determine a function only attaining the values 0 and 1) from Radon transform data. Standard inversion method for the Radon trans...

The inversion of the one–dimensional Radon transform on the rotation group SO(3) is an ill posed inverse problem which applies to X–ray tomography with polycrystalline materials. This communication presents a novel approach to the numerical inversion of the one–dimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete inverse Radon transform of a function sampled on th...