Fourier properties of the fan-beam sinogram.
OBJECTIVE
P. R. Edholm, R. M. Lewitt, and B. Lindholm, "Novel properties of the Fourier decomposition of the sinogram," in Proceedings of the International Workshop on Physics and Engineering of Computerized Multidimensional Imaging and Processing [Proc. SPIE 671, 8-18 (1986)] described properties of a parallel beam projection sinogram with respect to its radial and angular frequencies. The purpose is to perform a similar derivation to arrive at corresponding properties of a fan-beam projection sinogram for both the equal-angle and equal-spaced detector sampling scenarios.


METHODS
One of the derived properties is an approximately zero-energy region in the two-dimensional Fourier transform of the full fan-beam sinogram. This region is in the form of a double-wedge, similar to the parallel beam case, but different in that it is asymmetric with respect to the frequency axes. The authors characterize this region for a point object and validate the derived properties in both a simulation and a head CT data set. The authors apply these results in an application using algebraic reconstruction.


RESULTS
In the equal-angle case, the domain of the zero region is (q,k) for which / k/(k-q) / > R/L, where q and k are the frequency variables associated with the detector and view angular positions, respectively, R is the radial support of the object, and L is the source-to-isocenter distance. A filter was designed to retain only sinogram frequencies corresponding to a specified radial support. The filtered sinogram was used to reconstruct the same radial support of the head CT data. As an example application of this concept, the double-wedge filter was used to computationally improve region of interest iterative reconstruction.


CONCLUSIONS
Interesting properties of the fan-beam sinogram exist and may be exploited in some applications.
Mazin
Samuel R
SR
Department of Radiology, Stanford University, Stanford, California 94305, USA. smazin@stanford.edu
Pelc
Norbert J
NJ
D000465:Algorithms; D003198:Computer Simulation; D003201:Computers; D005583:Fourier Analysis; D006257:Head / Q000000981:diagnostic imaging; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000295:instrumentation / Q000379:methods; D014057:Tomography, X-Ray Computed / Q000379:methods*