TY - GEN
T1 - New extended fan-beam reconstruction formula
AU - Wang, Ge
AU - Lin, T. H.
AU - Cheng, Ping Chin
PY - 1992
Y1 - 1992
N2 - Because of its high imaging efficiency, fan-beam reconstruction approach has been very popular in recent years. However, fan-beam reconstruction formula had been restricted to a circular scanning locus until an extended fan-beam reconstruction formula was presented by D. B. Smith. Actually, non-circular scanning loci are not only academically interesting, but also practically significant. We propose a new extended fan-beam reconstruction formula, which is obtained based on geometrical intuition and is then validated by a strict mathematical proof. The new fan-beam reconstruction formula is the same as the conventional equispatial one, except that the source-to-origin distance depends on the rotation angle, and thus gets rid of the derivative of a locus and always requires a spatially invariant convolution. Furthermore, due to its simple form, the new formula naturally results in a unified discrete version. The new formula requires that the source-to-origin distance be differentiable almost everywhere with respect to the rotation angle and be symmetric with respect to the origin of the reconstruction coordinate system. The numerical simulation results of the new fan-beam formula are also presented.
AB - Because of its high imaging efficiency, fan-beam reconstruction approach has been very popular in recent years. However, fan-beam reconstruction formula had been restricted to a circular scanning locus until an extended fan-beam reconstruction formula was presented by D. B. Smith. Actually, non-circular scanning loci are not only academically interesting, but also practically significant. We propose a new extended fan-beam reconstruction formula, which is obtained based on geometrical intuition and is then validated by a strict mathematical proof. The new fan-beam reconstruction formula is the same as the conventional equispatial one, except that the source-to-origin distance depends on the rotation angle, and thus gets rid of the derivative of a locus and always requires a spatially invariant convolution. Furthermore, due to its simple form, the new formula naturally results in a unified discrete version. The new formula requires that the source-to-origin distance be differentiable almost everywhere with respect to the rotation angle and be symmetric with respect to the origin of the reconstruction coordinate system. The numerical simulation results of the new fan-beam formula are also presented.
UR - https://www.scopus.com/pages/publications/0026983579
M3 - Conference contribution
AN - SCOPUS:0026983579
SN - 081940814X
T3 - Proceedings of SPIE - The International Society for Optical Engineering
SP - 262
EP - 273
BT - Proceedings of SPIE - The International Society for Optical Engineering
PB - Publ by Int Soc for Optical Engineering
T2 - Biomedical Image Processing and Three-Dimensional Microscopy. Part 1 (of 2)
Y2 - 10 February 1991 through 13 February 1991
ER -