## 3 Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Sampling Ratio**} & **0.4** & **0.6** & **0.8** & **1** \\ \hline \multirow{3}{*}{Figure 1} & SART & — & 0.9499 \(\pm\) 0.0015 & 0.9615 \(\pm\) 0.0018 & 0.9703 \(\pm\) 0.0016 \\  & SART + TV & — & 0.9661 \(\pm\) 0.0012 & 0.9682 \(\pm\) 0.0015 & 0.9841 \(\pm\) 0.0026 \\  & Wavelet & — & 0.9765 \(\pm\) 0.0012 & 0.9771 \(\pm\) 0.0011 & 0.9868 \(\pm\) 0.0014 \\  & Proposed approach & 0.9751 \(\pm\) 0.013 & 0.9838 \(\pm\) 0.0009 & 0.9858 \(\pm\) 0.0012 & 0.9931 \(\pm\) 0.0009 \\ \hline \multirow{3}{*}{Figure 2} & SART & — & 0.9461 \(\pm\) 0.0056 & 0.9607 \(\pm\) 0.0038 & 0.9771 \(\pm\) 0.0055 \\  & SART + TV & — & 0.9553 \(\pm\) 0.0078 & 0.9674 \(\pm\) 0.0045 & 0.9833 \(\pm\) 0.0076 \\  & Wavelet & — & 0.9687 \(\pm\) 0.0052 & 0.9763 \(\pm\) 0.0060 & 0.9842 \(\pm\) 0.0098 \\  & Proposed approach & 0.9743 \(\pm\) 0.0034 & 0.9830 \(\pm\) 0.0045 & 0.9850 \(\pm\) 0.0032 & 0.9923 \(\pm\) 0.0026 \\ \hline \multirow{3}{*}{Figure 3} & SART & — & 0.9254 \(\pm\) 0.0089 & 0.9451 \(\pm\) 0.0085 & 0.9583 \(\pm\) 0.0090 \\  & SART + TV & — & 0.9348 \(\pm\) 0.0078 & 0.9682 \(\pm\) 0.0091 & 0.9723 \(\pm\) 0.0089 \\  & Wavelet & — & 0.9578 \(\pm\) 0.0052 & 0.9789 \(\pm\) 0.0067 & 0.9815 \(\pm\) 0.0064 \\  & Proposed approach & 0.9451 \(\pm\) 0.0031 & 0.9687 \(\pm\) 0.0029 & 0.9812 \(\pm\) 0.0032 & 0.9994 \(\pm\) 0.0037 \\ \hline \multirow{3}{*}{Figure 4} & SART & — & 0.9491 \(\pm\) 0.0026 & 0.9707 \(\pm\) 0.0034 & 0.9795 \(\pm\) 0.0045 \\  & SART + TV & — & 0.9553 \(\pm\) 0.0045 & 0.9774 \(\pm\) 0.0034 & 0.9833 \(\pm\) 0.0044 \\  & Wavelet & — & 0.96 07 \(\pm\) 0.0022 & 0.9812 \(\pm\) 0.0023 & 0.9901 \(\pm\) 0.0024 \\  & Proposed approach & 0.9643 \(\pm\) 0.0023 & 0.9730 \(\pm\) 0.0021 & 0.9879 \(\pm\) 0.0032 & 0.9952 \(\pm\) 0.0027 \\ \hline \end{tabular}
\end{table} 
Table 3: Structural similarity index metric (SSIM) average performance comparison of the proposed algorithm with a series of algorithms, namely, SART [3], SART + TV [13], Patch + ordering Wavelet [14]. Table 2 presents an average performance comparison of the proposed approach with a set of image reconstruction algorithms. SART [3] is a popular iterative image reconstruction method, and it is effective in the case of high compressive sensing ratio. The other two methods are TV transform [13] and wavelet transform [14]. The above average performance for four methods are the average values over 10 times repetitions. They are suitable for low sampling ratio. Therefore, when the influence of point spread function exists, the performance of the three methods can be compared. As shown in Table 3, the structural similarity index is improved compared to the traditional methods. All kinds of objective image quality metrics have been improved in different compressive sensing ratio. In the case of very low sampling ratio, other algorithms cannot reconstruct images, but the proposed algorithm can achieve relatively good performance. Of course, the quality of the reconstructed image at low sampling ratio has decreased compared with that at high sampling ratio. SSIM is a full reference metric that requires two images from the same image capture--a reference image and a processed image. It actually measures the perceptual difference between two similar images. It cannot judge which of the two is better. In other words, the closer the reconstructed image is to the real image, the better the reconstructed image is. The proposed method shows acceptable performance for sampling ratio greater than 0.4 and exhibits similar fluctuations over increasing sampling ratio. On the other hand, other algorithms have relatively good performance over high ratios. However, when the ratio is less than or equal to 0.4, the image performance is unacceptable. The lower sampling ratio is, the fewer data used for image reconstruction is. The fewer data for reconstructed images means less radiation dose for patients.