Cone-beam reconstruction using 1D filtering along the projection of M -lines

Abstract

In this paper, three exact formulae are derived for cone-beam reconstruction with source positions on a curve or set of curves. For reconstruction at a single point, these formulae all operate by applying a filtration step followed by a backprojection step to cone-beam data. The filtering is performed along a 1D curve which is defined as the intersection of the detector surface with a filtering plane. Two of these formulae allow a flexibility in the choice of the filtering direction. In some cases, this flexibility allows the efficiency of volume reconstruction to be improved. Alternatively, the flexibility can be used to reduce the detector size necessary to avoid truncation artefacts in the reconstruction or to change the noise properties of the reconstruction.

Cone-Beam Tomography with Linearly Distorted Source Trajectories

“…During simulation studies, we were able to achieve high quality image reconstructions from an ellipseplus-oblique-line trajectory by involving two theoreticallyexact reconstruction algorithms arising from Katsevich's general CB inversion scheme. To our knowledge, another accurate reconstruction approach [8] can deal with distorted source trajectories more naturally. However, this algorithm may have drawbacks in terms of data utilization and detector requirements compared to the presented strategies.…”

Noise Properties of Chord-Image Reconstruction

“…The chord-based FBP algorithm [6], [10] can be expressed as (9) where indicates the cone-beam projection of onto the detector and is determined by using to replace in (8), and denotes the distance from the source point to a point on the detector at which the ray connecting and intersects the detector. As the filtering (i.e., the integration over ) is carried out over the projection of the straight line containing the chord, similar to other existing FBP-based algorithms, the chord-based FBP algorithm cannot exactly reconstruct ROI images from data containing transverse truncations.…”

“…Some of these algorithms can reconstruct images within 3-D regions of interest (ROIs) from cone-beam data containing both longitudinal and transverse truncations. The introduction of the -line concept and reconstruction [5], [9] provides additional flexibility for covering volume ROIs.…”

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] …”

“…Thus, the Tuy-Grangeat stable reconstruction conditions [24], [25] at a point x will be read on the virtual trajectory Γ t ( a(t)), just as the possibility to use modern 3D CB reconstruction algorithms [26], [7], [27].…”