Image reconstruction on virtual PI-lines using filtered-backprojection in circular cone-beam CT

Recently, a 3D filtered-backprojection(FBP)-based algorithm for image reconstruction on PI-line segments in a helical cone-beam CT scan has been developed (Zou and Pan, 2004). In the present work, we derive new reconstruction algorithms for circular cone-beam scans based upon this algorithm and a concept of virtual PI-line. We prove that, in the case of conventional full- and short-scan, the newly derived algorithms are mathematically identical to existing algorithms. More importantly, in the case of reduced-scans in which the scanning angle range is less than that in a short-scan, the new algorithms can yield exact region of interest (ROI) reconstruction in mid-plane and approximate ROI reconstruction in off-mid-planes. We have performed a preliminary numerical study that verifies our theoretical assertions.