A local shift‐variant Fourier model and experimental validation of circular cone‐beam computed tomography artifacts

Abstract

Large field of view cone-beam computed tomography ͑CBCT͒ is being achieved using circular source and detector trajectories. These circular trajectories are known to collect insufficient data for accurate image reconstruction. Although various descriptions of the missing information exist, the manifestation of this lack of data in reconstructed images is generally nonintuitive. One model predicts that the missing information corresponds to a shift-variant cone of missing frequency components. This description implies that artifacts depend on the imaging geometry, as well as the frequency content of the imaged object. In particular, objects with a large proportion of energy distributed over frequency bands that coincide with the missing cone will be most compromised. These predictions were experimentally verified by imaging small, localized objects ͑acrylic spheres, stacked disks͒ at varying positions in the object space and observing the frequency spectrums of the reconstructions. Measurements of the internal angle of the missing cone agreed well with theory, indicating a right circular cone for points on the rotation axis, and an oblique, circular cone elsewhere. In the former case, the largest internal angle with respect to the vertical axis corresponds to the ͑half͒ cone angle of the CBCT system ͑typically ϳ5°-7.5°in IGRT͒. Object recovery was also found to be strongly dependent on the distribution of the object's frequency spectrum relative to the missing cone, as expected. The observed artifacts were also reproducible via removal of local frequency components, further supporting the theoretical model. Larger objects with differing internal structures ͑cellular polyurethane, solid acrylic͒ were also imaged and interpreted with respect to the previous results. Finally, small animal data obtained using a clinical CBCT scanner were observed for evidence of the missing cone. This study provides insight into the influence of incomplete data collection on the appearance of objects imaged in large field of view CBCT.

A new method to combine 3D reconstruction volumes for multiple parallel circular cone beam orbits

“…It is known that in any region of the image, FDK correctly reconstructs the measured spatial frequencies ͑i.e., those outside the missing cone͒. 10 Since each source has a divergent beam, there is an overlap volume that can be reconstructed from multiple sources as shown in Fig. 3͑b͒.…”

“…[7][8][9][10][11][12] For a brief description, consider a single impulse object on the z-axis but off the central plane ͓Fig. 1͑a͔͒.…”

“…4͑b͔͒ in frequency space and the size of the missing cone region is determined by the tilt angle of each source for the point. For any volume, since the outside of the missing cone region is reconstructed correctly, 10 this information can be utilized to improve the noise performance using weighted averaging in frequency space FIG. 4.…”

Deformable image registration and interobserver variation in contour propagation for radiation therapy planning

“…Studies have assessed the accuracy of DIR algorithms using digital phantoms, (10) physically deforming phantoms, (11) mathematical descriptors, 12 , 13 and clinical CT scans 14 , 15 , 16 . Digital (10) or physically deforming phantom studies, (11) while useful, may lack clinical complexity.…”

“…Digital (10) or physically deforming phantom studies, (11) while useful, may lack clinical complexity. Mathematical descriptors, such as curl and the Jacobian, have been proposed as useful metrics to quantify the deformation vector field 12 , 13 .…”