Inversion of incomplete cone-beam data

Implementation of Tuy's cone-beam inversion formula.

Tuy's cone-beam inversion formula was modified to develop a cone-beam reconstruction algorithm. The algorithm was implemented for a cone-beam vertex orbit consisting of a circle and two orthogonal lines. This orbit geometry satisfies the cone-beam data sufficiency condition and is easy to implement on commercial single photon emission computed tomography (PECT) systems. The algorithm, which con...

A general inversion formula for cone beam CT

We present a new cone beam inversion formula based on a general weighting function n. The formula is theoretically exact and is represented by a 2D integral. If the source trajectory C is complete (and satisfies two other very mild assumptions), then the simplest uniform weight gives a convolution-based FBP algorithm. This choice is not always optimal from the practical point of view. The unifo...

An Inversion Method for the Cone-Beam Transform

This paper presents an alternative formulation for the cone-beam projections given an arbitrary source trajectory and detector orientation. This formulation leads to a new inversion formula. As a special case, the inversion formula for the spiral source trajectory is derived.

An Improved Exact Inversion Formula for Cone Beam Vector Tomography

In this article we present an improved exact inversion formula for the 3D cone beam transform of vector fields. It is well known that only the solenoidal part of a vector field can be determined by the longitudinal ray transform of a vector field in cone beam geometry. The exact inversion formula, as it was developed in A. Katsevich and T. Schuster, An exact inversion formula for cone beam vect...

Image Reconstruction from Incomplete Data