Reconstruction Algorithm for Fan Beam with a Displaced Center-of-Rotation

Grant T. Gullberg, Carl R. Crawford, Benjamin M.W. Tsui

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


A convolutional backprojection algorithm is derived for a fan beam geometry that has its center-of-rotation displaced from the midline of the fan beam. In single photon emission computedtomography (SPECT), where a transaxial converging collimator is used with a rotating gamma camera, it is difficult to precisely align the collimator so that the mechanical center-of-rotation is colinear with the midline of the fan beam. A displacement of the center-of-rotation can also occur in X-ray CT when the X-ray source is mispositioned. Standard reconstruction algorithms which directly filter and backproject the fan beam data without rebinning into parallel beam geometry have been derived for a geometry having its center-of-rotation at the midline of the fan beam. However, in the case of a misalignment of the center-of-rotation, if these Conventional reconstruction algorithms are used to reconstruct the fan beam projections, structured artifacts and a loss of resolution will result. We illustrate these artifacts with simulations and demonstrate how the new algorithm corrects for thismisalignment. We also show a method to estimate the parameters of the fan beam geometry including the shift in the center-of-rotation.

Original languageEnglish (US)
Pages (from-to)23-29
Number of pages7
JournalIEEE transactions on medical imaging
Issue number1
StatePublished - Mar 1986
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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