## 3 Simulation Results
### Noise Robustness  
In practical applications, the detected signals are vulnerable to the interference of thermal noise, which is usually Gaussian. Therefore, it is of great importance to test the noise robustness of the algorithm. White Gaussian noise with different powers is added to the detected signals for the case of 20-points straight-line scanning. Then, three groups of noisy signals are acquired with a signal to noise ratio (SNR) of 10 dB, 5 dB and 0 dB, respectively.  
The reconstructed images for the three algorithms from the noise-polluted signals are shown in Figure 9. Results show that the TV-GPEF has stronger noise resistance than the other two algorithms. The images from the noisy signals are very close to those from the noise-free signals. Light absorbers in images are clear and distinguishable. The detailed information is quite consistent with the original image. The background noise is well suppressed and there is no significant effect of the added noise to the reconstructed image. However, for the TV-VB and the TV-GD, the added noise has a great influence on the reconstructed images. For the TV-VB, a certain degree of fuzziness appears which blurs the edges of the optical absorbers and there is a lot of background noise in the reconstructed  
Figure 8: The reconstructed images from the limited-angle circular scanning by the TV-GD, TV-VB and TV-GPEF algorithms: the first row refers to the results of the TV-GD (**a–c**); the second row refers to the results of the TV-VB (**d–f**); and the third row refers to the results of the TV-GPEF (**g–i**). The first to third columns refer to the results from: 60-views (**a,d,g**); 90-views (**b,e,h**); and 120-views (**c,f,i**) sampling, respectively.  
images. The effects of noise are even worse when the SNR decreases. For the result for 0 dB SNR, serious artifacts fuzz up the reconstructed image, which seriously debases the quality of the image. For the TV-GD, the image is severely affected by the added noise and almost all light absorbers are damaged in the reconstructed results.  
The PSNRs of the reconstructed images from the noise-added signals for the three algorithms are displayed in Table 3. From the table we can see that the TV-GPEF algorithm outperforms other two algorithms. The PSNR of the TV-GPEF is about 11 dB higher than that of the TV-VB and about 8 dB higher than that of the TV-GD on average. Therefore, we can get the conclusion that the TV-GPEF has the strongest noise robustness compared to the other two algorithms.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**PSNRs (dB)** & **0 dB** & **5 dB** & **10 dB** \\ \hline
**TV-GD** & 12.59 & 13.47 & 14.02 \\
**TV-VB** & 14.97 & 16.49 & 18.55 \\
**TV-GPEF** & 21.38 & 25.32 & 27.39 \\ \hline \hline \end{tabular}
\end{table}
Table 3: PSNR (dB) of the reconstruction from the noise-added signals.  
Figure 9: The reconstructed images from the noise-added signals by the TV-GD, TV-VB and TV-GPEF algorithms: the first row refers to the results of the TV-GD (**a–c**); the second row refers to the results of the TV-VB (**d–f**); and the third row refers to the results of the TV-GPEF (**g–i**). The first to third columns refer to the results from SNR of: 10 dB (**a**,**d**,**g**); 5 dB (**b**,**e**,**h**); and 0 dB (**c**,**f**,**i**) sampling, respectively.