Table 1.
Difference of three backprojection based methods.
Fig 1.
A one-dimensional detector-bin measures an integral of attenuation along the line at angle θ and distance r to the isocenter.
Fig 2.
(A) in the spatial space; (B) its corresponding PSF.
Fig 3.
An example of constructing a weighted filter with 36 projections.
(A) common ramp filter; (B) projection trajectories; (C) weighted ramp filter. To emphasize the visual effect of weight, the elements not on the projection trajectories are set to 0.
Fig 4.
The two test images used in this paper.
(A) NCAT phantom [34] with simple features; (B) real CT image with complex features. Both images are 2048 × 2048 pixels and normalized to a display window [0, 1].
Fig 5.
SNR performance with different α.
Fig 6.
SNR performance with different σ.
Fig 7.
Performance comparison of different methods based on simulations.
(A) SNR performance; (B) reconstruction time.
Fig 8.
Visual comparison using 180 projections.
(A) original image with Gaussian noise; (B) FBP; (C) BPF; (D) BPF-W; (E) BPWD; (F) BPWD-W.
Fig 9.
Partial line (indicated by red line in Fig 8) profiles (normalised to the same maximum value) using 180 projections.
(A) original image with Gaussian noise; (B) FBP; (C) BPF; (D) BPF-W; (E) BPWD; (F) BPWD-W.
Table 2.
SNR (dB) performance of different methods.
Fig 10.
Sparse-view reconstructions with 180 projections from different methods.
FBP with (A) ramp, (B) Shepp-Logan, or (C) Hann filter; FBP with Hann filter then Wiener noise-removal filtering with a window size of (D) 5 or (E) 10; BPWD-W with (F) σ = 1, (G) σ = 7, or (H) σ = 15.
Fig 11.
Comparison of reconstructions between FBP and BPWD-W with 1800 projections.
FBP with (A) ramp, (B) Shepp-Logan, or (C) Hann filter; BPWD-W with (D) σ = 1, (E) σ = 7, or (F) σ = 15.
Fig 12.
Canny edge enhancement using (Fig 11D and 11F).
Note that the white fringes around the air containing structures are characteristic of the propagation-based synchrotron PCXI setup.