This study reviews the theory, programming designs and merits of two new Matlab-based routines for the forward and inverse Radon transform. These routines offer users flexible choices of integration path functions to take advantage of improved Radon-domain identification and isolation of seismic phases. Least-squares inversion of frequency components and judicious choices of regularization tech...

Abstract. The Fourier slice theorem used for the standard Radon transform generalizes to a Laplace counterpart when considering the exponential Radon transform. We show how to use this fact in combination with using algorithms for unequally spaced fast Laplace transforms to construct fast and accurate methods for computing, both the forward exponential Radon transform and the corresponding back...

introduction: diabetic retinopathy (dr) is one of the most serious and most frequent eye diseases in the world and the most common cause of blindness in adults between 20 and 60 years of age. following 15 years of diabetes, about 2% of the diabetic patients are blind and 10% suffer from vision impairment due to dr complications. this paper addresses the automatic detection of microaneurysms (ma...

in this paper, by considering a squint angle for synthetic aperture radar in the strip-map mode, a method is proposed for estimating parameters of a fixed acceleration moving target. non-zero doppler centroid and range-azimuth coupling in the squint mode add complexity to estimation equations of moving target parameters and cause doppler ambiguity. this, in turn, causes to lose the efficiency o...

The Radon transform in combination with self-organizing maps is used to build the rotation invariant systems for categorization of visual objects. The first system has one SOM per the Radon transform direction. The outputs from these directional SOMs that represent positions of the winners and related post-synaptic activities, form the input to the final categorizing SOM. Such a network deliver...

The representation of a function by its circular Radon transform (CRT) and various related problems arise in many areas of mathematics, physics and imaging science. There has been a substantial spike of interest towards these problems in the last decade mainly due to the connection between the CRT and mathematical models of several emerging medical imaging modalities. This paper contains some n...

We consider the X-ray transform in a projective space over a finite field. It is well known (after E. Bolker) that this transform is injective. We formulate an analog of I.M. Gelfand’s admissibility problem for the Radon transform, which asks for a classification of all minimal sets of lines for which the restricted Radon transform is injective. The solution involves doubly ruled quadric surfaces.

We interpret the setting for a Radon transform as a submanifold of the space of generalized functions, and compute its extrinsic curvature: it is the Hessian composed with the Radon transform. 1. The general setting. Let M and Σ be smooth finite dimensional manifolds. Let m = dim(M). A linear mapping R : C∞ c (M)→ C∞(Σ) is called a (generalized) Radon transform if it is given in the following w...

In this paper the discrete generalized Radon transform will be investigated as a tool for detection of curves in noisy digital images. The discrete generalized Radon transform maps an image into a parameter domain, where curves following a specific parameterized curve form will correspond to a peak in the parameter domain. A major advantage of the generalized Radon transform is that the curves ...

This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distri...