A simple method for tomography reconstruction

Figures & data

Figure 1. Ray attenuation path.

Figure 2. Real obstacle, approximate model and projection example.

Table

Algorithm 1: Image reconstruction based on sensitivity analysis
Require: Projection data p*, matrix K, step size δμ and tol.
Ensure: The reconstructed image μ.
set μ^0 = 0, t = 0, Stop = FALSE
while Stop = FALSE do
compute gΨ^t using Eq. (8)
for every cell i do
if giΨ^t < 0 then
else
end if
if sign(giΨ^t)! = sign(giΨ^t−1) then
end if
end for
if |Ψ(μ^t) − Ψ(μ^t+1)| > tol then
t = t + 1
else
Stop = TRUE, μ = μ^t
end if
end while

Figure 3. Original data set used in tests.

Figure 4. Projection data for 16, 32, 64 and 128 directions. The abscissa corresponds to p* for each direction and the ordinate to the d-th direction. The intensity scale is the same for all images.

Figure 5. Results for the gΨ reconstruction method. D = 16, 32, 64 and 128.

Figure 6. Objective function evolution for each case.

Figure 7. Projection data for PSNR 40 dB, 35 dB, 30 dB and 25 dB (128 directions). The abscissa corresponds to p* for each direction and the ordinate to the d-th direction.

Figure 8. Results for the gΨ reconstruction method from noise data with 128 directions for PSNR 40 dB, 35 dB, 30 dB and 25 dB (128 directions).

Figure 9. Objective function evolution for reconstruction with noise.

Figure 10. Projection data for different discretizations (1.1, 1.2, 1.3 and 1.4 spacings) and 128 directions. The abscissa corresponds to p* for each direction and the ordinate to the d-th direction.

Figure 11. Results for the gΨ reconstruction method for different discretization in the reconstructed image (1.1, 1.2, 1.3 and 1.4 spacings, 128 directions).

Figure 12. Objective function evolution for spacing 1.1, 1.2, 1.3 and 1.4.