  With advanced X-ray source and detector technologies being continuously
developed, non-traditional CT geometries have been widely explored.
Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an X-ray
source might be positioned radially far away from the focus of arced detector
array that is equiangularly spaced, is of importance in many novel CT systems
and designs. GEGCT, unfortunately, has no theoretically exact and
shift-invariant analytical image reconstruction algorithm in general. In this
study, to obtain fast and accurate reconstruction from GEGCT and to promote its
system design and optimization, an in-depth investigation on a group of
approximate Filtered BackProjection (FBP) algorithms with a variety of
weighting strategies has been conducted. The architecture of GEGCT is first
presented and characterized by using a normalized-radial-offset distance
(NROD). Next, shift-invariant weighted FBP-type algorithms are derived in a
unified framework, with pre-filtering, filtering, and post-filtering weights.
Three viable weighting strategies are then presented including a classic one
developed by Besson in the literature and two new ones generated from a
curvature fitting and from an empirical formula, where all of the three weights
can be expressed as certain functions of NROD. After that, an analysis of
reconstruction accuracy is conducted with a wide range of NROD. We further
stretch the weighted FBP-type algorithms to GEGCT with dynamic NROD. Finally,
the weighted FBP algorithm for GEGCT is extended to a three-dimensional form in
the case of cone-beam scan with a cylindrical detector array.
