A Framework for Discrete Integral Transformations II-The 2D Discrete Radon Transform

The Radon transform is a fundamental tool in many areas. For example, in reconstruction of an image from its projections (CT scanning). Although it is situated in the core of many modern physical computations, the Radon transform lacks a coherent discrete definition for 2D discrete images which is algebraically exact, invertible, and rapidly computable. We define a notion of 2D discrete Radon transforms for discrete 2D images, which is based on summation along lines of absolute slope less than 1. Values at non-grid locations are defined using trigonometric interpolation on a zero-padded grid. The discrete 2D definition of the Radon transform School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel Department of Mathematics, Yale University, New Haven, Connecticut 06520 Statistics Department, Stanford University, Stanford, CA 94305 Faculty of Computer Science, Technion, Haifa 32000, Israel Department of Mathematics, Yale University, New Haven, Connecticut 06520 School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel