Inverse Radon Transform at Work

Solving the Inverse Radon Transform for Vector Field Tomographic Data

It is widely recognised that the most popular manner of image representation is obtained by using an energy-preserving transform, like the Fourier transform. However, since the advent of computerised tomography in the 70s, another manner of image representation has also entered the center of interest. This new type is the projection space representation, obtained via the Radon transform. Method...

Radon transform and curvature

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...

Discrete radon transform

This paper describes the discrete Radon transform (DRT) and the exact inversion algorithm for it. Similar to the discrete Fourier transform (DFT), the DRT is defined for periodic vector-sequences and studied as a transform in its own right. Casting the forward transform as a matrix-vector multiplication, the key observation is that the matrix-although very large-has a block-circulant structure....

The Radon-gauss Transform

Gaussian measure is constructed for any given hyperplane in an infinite dimensional Hilbert space, and this is used to define a generalization of the Radon transform to the infinite dimensional setting, using Gauss measure instead of Lebesgue measure. An inversion formula is obtained and a support theorem proved.

Accuracy in radon work.