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 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...

Generalized Radon transforms such as the hyperbolic Radon transform cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We introduce a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise low-rank ap...

The discrete Radon transform is a useful tool in image processing for detection of lines (or in general curves) in digital images. One of the key properties of the discrete Radon transform is that a line in an image is transformed into a peak in the parameter domain, where the position of the peak corresponds to the line parameters. What often is needed, is to determine whether a Radon transfor...

In this work a new offline signature recognition system based on Radon Transform, Fractal Dimension (FD) and Support Vector Machine (SVM) is presented. In the first step, projections of original signatures along four specified directions have been performed using radon transform. Then, FDs of four obtained vectors are calculated to construct a feature vector for each signature. These vectors ar...