Analysis of an exact inversion algorithm for spiral cone-beam CT

Abstract

In this paper we continue studying a theoretically exact filtered backprojection inversion formula for cone beam spiral CT proposed earlier by the author. Our results show that if the phantom f is constant along the axial direction, the formula is equivalent to the 2D Radon transform inversion. Also, the inversion formula remains exact as spiral pitch goes to zero and in the limit becomes again the 2D Radon transform inversion formula. Finally, we show that according to the formula the processed cone beam projections should be backprojected using both the inverse distance squared law and the inverse distance law.

Noise Properties of Chord-Image Reconstruction

“…The projection data of the object function can be mathematically expressed as (1) where the unit vector denotes the direction of a specific X-ray passing through the point . We also introduce two additional coordinate systems and to describe the geometry in a general scan.…”

“…N recent years, exact algorithms have been developed for reconstructing images [1] and for reconstructing images on " -lines" [2]- [4] from helical cone-beam data. Since 2005, papers have being published on algorithm development for reconstructing images on chords for general trajectories [5]- [8].…”

Algebraic and analytic reconstruction methods for dynamic tomography

“…These last years, new developments have been proposed to solve analytically, exactly, and efficiently this problem, in particular for the helical source trajectory, but also for more general trajectory (see for exemple [3], [4], [5], [6], [7], [8] …”

Comparative evaluation of two analytical methods for Helical Cone-Beam Tomography

“…[1]- [4]. They can be divided into two groups: Mathematically exact methods and approximate methods.…”