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...

Three multiple attenuation techniques are tested on a Gulf of Mexico dataset. These methods are (1) a hyperbolic Radon transform followed by a mute (2), the Delft approach and (3), a pattern-based technique. The Radon transform separates multiples and primaries according to their moveout. The Delft approach models the multiples and subtracts them by estimating adaptive filters. The pattern-base...

In this paper we derive explicit inversion formulas for recovering scalar and vector fields supported on the unit disk from their 2D attenuated Radon transform in the framework of the fan-beam scanning geometry. The attenuation function is supposed to be known (from additional transmission measurements, for instance). It is known that in the vector case the kernel of the (unattenuated) Radon tr...

The purpose of this paper is to extend and clarify the methods of the papers [G1] and [G2] by using the methods of [G3], incorporating ideas from Carnot-Caratheodory geometry such as those of the fundamental paper [NSW]. We will thereby prove an analogue for singular Radon transforms to the T (1) theorem of David and Journe [DJ]. As in [G1] and [G2], we will associate a singular integral operat...