We define a notion of Radon Transform for data in an n by n grid. It is based on summation along lines of absolute slope less than 1 (as a function either of x or of y), with values at non-Cartesian locations defined using trigonometric interpolation on a zero-padded grid. The definition is geometrically faithful: the lines exhibit no 'wraparound effects'. For a special set of lines equispaced ...

Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Ra...

The Radon transform belongs to the area of Inverse Problems. The reconstruction of a function from its projection or averages is a central point of study. Besides having direct applications in medical tomography, geophysics, there are also applications in signal processing, statistics and probability. Hence, it is useful to consider discretized versions of the Radon transform.

This book is devoted to a discrete Radon transform named the Mojette transform. The Radon transform specificity is to mix Cartesian and radial views of the plane. However, it is straightforward to obtain a discrete lattice from a Cartesian grid while it is impossible from a standard equiangular radial grid. The only mathematical tool is to use discrete geometry that replaces the equiangular rad...

A method for producing a radar-reflectivity map of the polar regions of the Moon or a planet from polar orbit with only the frequency shift of the reflected signals is described and simulated. A Radon transform of the reflectivity is obtained during multiple passes over the pole. Inversion of this Radon transform enables a map of radar reflectivity to be synthesized.