Exact BPF and FBP algorithms for nonstandard saddle curves

Abstract

A hot topic in cone-beam CT research is exact cone-beam reconstruction from a general scanning trajectory. Particularly, a nonstandard saddle curve attracts attention, as this construct allows the continuous periodic scanning of a volume-of-interest (VOI). Here we evaluate two algorithms for reconstruction from data collected along a nonstandard saddle curve, which are in the filtered backprojection (FBP) and backprojection filtration (BPF) formats, respectively. Both the algorithms are implemented in a chord-based coordinate system. Then, a rebinning procedure is utilized to transform the reconstructed results into the natural coordinate system. The simulation results demonstrate that the FBP algorithm produces better image quality than the BPF algorithm, while both the algorithms exhibit similar noise characteristics.

Exact Interior Reconstruction from Truncated Limited‐Angle Projection Data

“…According to the results of Pack et al [13], the 1D Hilbert transform g ( x ) of f ( x ) can be exactly obtained on the interval [ c 3 , c 4 ]. Based on the inverse Hilbert Transform [2, 14], we have $\begin{array}{ll}& \sqrt{false(c_5-xfalse)false(x-c_{2}false)}ffalse(xfalse)\\ & \hspace{1em}\hspace{1em}\begin{array}{c}={{\displaystyle \int }}_{c_3}^{c_4}\frac{\sqrt{false(c_5-\tilde{x}\hspace{0.17em}false)false(\tilde{x}-c_{2}false)}gfalse(\tilde{x}false)}{\pi false(\tilde{x}-xfalse)}d\tilde{x}+\frac{1}{\pi }{{\displaystyle \int }}_{c_2}^{c_5}ffalse(\tilde{x}\hspace{0.17em}false)d\tilde{x}\end{array}\end{array}$ $\begin{array}{ll}& \hspace{1em}\hspace{1em}\hspace{1em}+\left({\int }_{c_2}^{c_3}+{\int }_{c_4}^{c_5}\right)\frac{d\tilde{x}\sqrt{false(c_5-\tilde{x}\hspace{0.17em}false)false(\tilde{x}-c_{2}false)}gfalse(\tilde{x}\hspace{0.17em}false)}{\pi false(\tilde{x}-xfalse)}\end{array}\mathrm{.}$ Note that (16) is known for any x ∈ ( c 2 , c 5 ), (…”

Onboard cone beam CT with flexible image trajectories to improve image quality and longitudinal coverage: simulation and phantom study

“…Further study on saddle-like trajectories [8] which could potentially allow one 360-roation to cover more longitudinal volume and still allow exact reconstruction.…”

Data Consistency Based Rigid Motion Artifact Reduction in Fan-Beam CT

“…If we assume that both and are smooth and continuous, we can approximate and with finite basis functions. Without loss of generality, we assume (25) By defining an objective function (26) with defined by (20), we transform the motion estimation problem into the following optimization problem (27) where is the motion parameter vector, a weighting function, and the highest order of the involved moments. Equation (27) is the fundamental formula for estimating the general in-plane motion based on the HLCC.…”