Affiliations: Department of Medical Physics, University of
Wisconsin-Madison, Madison, WI 53704, USA | Department of Radiology, University of
Wisconsin-Madison, Madison, WI 53792, USA
Note: [] Corresponding author: Guang-Hong Chen, PhD, Departments of
Medical Physics and Radiology, University of Wisconsin-Madison, J5/M174,
Clinical Science Center, 600 Highland Avenue, Madison, WI 53792-1590, USA.
Tel.: +1 608 263 0089; Fax: +1 608 265 9840; E-mail: [email protected]
Abstract: Conventionally, the FDK algorithm is used to reconstruct images in
many imaging systems where cone-beam projections are acquired from a single
circular scanning path in a 2π angular range (full scan
mode) and has been heuristically extended to a π+fan angle
angular range (short-scan mode). In this paper, a new cone-beam reconstruction
algorithm is derived for a single arc source trajectory with an equal weighting
scheme. This algorithm is derived in the Katsevich framework. Since the single
arc does not satisfy Tuy's data sufficiency condition, the resulting algorithm
is an approximate reconstruction algorithm. The feature of one-dimensional (1D)
shift-invariant filtering in the conventional FDK algorithm is nicely
preserved. The new algorithm includes a voxel dependent backprojection step of
weighted combinations of 1D Hilbert filtered data, after an initial
differentiation operation. In comparing the new algorithm with the standard
FDK: the new algorithm intrinsically handles full scan, short scan and
super-short scan modes. Numerical simulations have been performed to validate
the algorithm, and demonstrate more quantitatively correct density values when
reconstructing points away from the central slice. Noise performance was
assessed for both the new algorithm and the FDK algorithm using simulated
Poisson noise.
