## 4 In Vitro Experiment  
In-vitro experiments were also conducted to validate the effectiveness of the proposed TV-GPEF algorithm. Limited-angle circular scanning with 180-views, 90-views and 60-views as well as straight-line scanning were carried out and the reconstructed results for three algorithms were compared and discussed. The platform for the experiment is shown in Figure 11. The laser we use was a Nd:YAG laser device ( Surelite I, Continuum, San Jose, CA, USA). The laser pulse with the wavelength of 532 nm was irradiated from the device and reflected by a mirror. Then, it is expanded by a concave mirror and illuminates the object uniformly. The duration of the laser was 4-6 ns and the frequency was 10 Hz. The settings of the laser meeted the American National Standards Institute (ANSI) laser radiation safety standard. The photoacoustic signals were detected by a transducer (V383-SU, Panametrics, Waltham, MA, USA) driven by a stepping motor to scan around the imaged object. The center frequency of the transducer was 3.5 MHz and the bandwidth was 1.12 MHz. The sampling rate of the system was 16.67 MHz. The phantom for the limited-angle circular scanning is shown in Figure 12a. The phantom was made of a gelatin cylinder which had very small light absorption coefficient. The light absorbers were one leaf embedded into the gelatin cylinder. The radius of the phantom was 25 mm. The shape of the phantom imitated the structure of the blood vessel and tissue. The sampling interval was 2\({}^{\circ}\). The 180-views, 90-views and 60-views scanning were conducted, corresponding to the sampling points of 90, 45 and 30, respectively. The scanning radius was 38 mm. The results of the reconstruction for three algorithms are shown in Figure 13. It can be indicated from the results that for the TV-GD, especially when the number of missing views become large, there is serious artifacts and blurs on the reconstructed images. For 90-views and 60-views scanning, almost no useful information for the phantom can be acquired from the results but a blur. For the TV-VB, the performance is improved \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time (s)** & **180-Views** & **90-Views** & **60-Views** \\ \hline
**TV-GD** & 15.68 & 13.73 & 10.32 \\
**TV-VB** & 9.87 & 8.37 & 6.14 \\
**TV-GPEF** & 16.43 & 14.46 & 11.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computation cost for the reconstruction from limited-angle circular scanning. Figure 11: Scheme of the platform used for the experiments. with respect to the TV-GD. However, there still exist a lot of artifacts in the missing views and edges of the light absorbers are not distinct enough which decreases the resolution of the image. Besides, the background noise also seriously reduces the contrast of the images thus affects the quality of the reconstruction. However for the TV-GPEF, the results are greatly improved. The background noise and the artifacts are suppressed well. The edges of the light absorber are enhanced and the contrast of the image is improved. Therefore, it can be concluded that the performance of the TV-GPEF precedes the two other algorithms in terms of the limited-angle circular scanning. Figure 12: Pictures of the phantoms used in the experiments: (**a**) for the limited-angle circular scanning; and (**b**) for the straight-line scanning. Figure 13: The reconstructed images from the phantom in Figure 10 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 the limited-angle circular scanning of: 60-views (**a**,**d**,**g**); 90-views (**b**,**e**,**h**); and 180-views (**c**,**f**,**i**) sampling, respectively. The straight-line scanning was also conducted to verify the proposed algorithm. The phantom for the straight-line scanning is shown in Figure 13b.