## 3 Main Scheme
### Algorithm III. Meaningful Shares Scheme
\begin{table}
\begin{tabular}{c c c c c c c} \hline \(\gamma\) & **Image** & **Method 1** & **Method 2** & **Method 3 * & **Method 4** \\ \hline \multirow{2}{*}{1} & shares & 10.08540 & 10.08555 & 10.08565 & 7.21653 \\ \cline{2-6}  & Restored image & 6.12667 & 3.01978 & inf & 3.03151 & 1.10599 \\ \hline \multirow{2}{*}{0.7} & shares & 6.59821 & 6.59845 & 6.59842 & 4.64744 \\ \cline{2-6}  & Restored image & 7.60584 & 4.59838 & 27.66252 & 4.66005 & 2.65272 \\ \hline \multirow{2}{*}{0.5} & shares & 5.23130 & 5.23122 & 5.23126 & 4.61973 \\ \cline{2-6}  & Restored image & 9.03888 & 6.07030 & 25.54497 & 6.08073 & 4.10810 \\ \hline \multirow{2}{*}{0.3} & shares & 4.22439 & 4.22448 & 4.22460 & 3.88114 \\ \cline{2-6}  & Restored image & 11.15357 & 8.10970 & 23.99535 & 8.19519 & 6.36929 \\ \hline \multirow{2}{*}{0} & shares & 3.01179 & 3.01144 & 3.01125 & 3.01124 \\ \cline{2-6}  & Restored image & 22.54548 & 22.54521 & 22.55623 & 22.55617 & 22.5452 \\ \hline \end{tabular}

* The PSNR values of the restored images are different in Method 3. The restored image on the left in this column is the first image, and on the right is the second image.

\end{table} 
Table 3: The PSNR analysis of the proposed schemes. ### Sensitivity and SSIM Analysis

PSNR is mainly for calculating the image distortion rating data, and sometimes it does not fully represent the human visual perception. Numerous experimental findings indicate that the visual quality perceived by the human eye and PSNR numbers do not always match up completely. In fact, higher PSNR scores may appear worse than lower PSNR scores. Therefore, we will introduce Sensitivity in this subsection. In the sensitivity analysis, we focus on the restoration of black pixels, called a black pixel in a restored image positive; \(N_{TP}\) and \(N_{FN}\) represent the number of pixels with the \"true positive\" and \"false negative\" features in the restored image. A pixel that is black in the original image is called a \"true positive\" pixel if it is still black after restoration; on the other hand, a pixel that is black in the original image is called a \"false negative\" pixel if it is restored to white. The formula for Sensitivity is given below:

\[Sensitivity=\frac{N_{TP}}{N_{TP}+N_{FN}} \tag{5}\]

We perform Sensitivity analysis for each of our proposed methods with \(p=45\), \(N=2\), and \(n=5\) in different \(\gamma\), then present the results together. A total of 7! (=5040) experimental results were averaged and given in Table 4.

The structural similarity index (SSIM) is a technique for calculating how two similar images are in terms of structure, contrast, and luminance. SSIM takes the value range [0, 1], and the higher the value, the lower the image distortion. Compared with the traditional image quality measurement standards, SSIM is more consistent with the human vision judgment of image quality. Given an original image \(I\) of size \(w\times h\) and a reconstructed image \(K\), we calculate the average value \(E(I)\) in image \(I\), the average value \(E(K)\) in image \(K\), and the three variances \(S_{I}\), \(S_{K}\), \(S_{IK}\) by using the formula demonstrated below. A constant term \(c_{1}\) is set equal to \(\left(K_{1}\times L\right)^{2}\) and \(c_{2}\) is set equal to \(\left(K_{2}\times L\right)^{2}\). Set the black pixel to 0, white pixel to 255, \(K_{1}\) to 0.01, \(K_{2}\) to 0.03, and \(L\) to 255, to avoid a denominator of 0 and keep it stable. The formula of the SSIM is given below:

\[SSIM(I,K)=\frac{2\times E(I)\times E(K)+c_{1}}{E(I)^{2}+E(K)^{2}+c_{1}}\times \frac{2\times S_{IK}+c_{2}}{S_{I}^{2}+S_{K}^{2}+c_{2}} \tag{6}\]

\[E(I)=\frac{1}{w\times h}\sum_{i=1}^{w\times h}I_{i} \tag{7}\]