# Image Restoration Using a Fixed-Point Method for a TVL2 Regularization Problem
## 7 Numerical Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Blur** & \(\mathbf{P_{0}}\) & **Alg** & \(\boldsymbol{\alpha}\) & \(\boldsymbol{\beta}\) & \(\boldsymbol{\gamma}\) & \(\boldsymbol{\lambda}\) & \(\boldsymbol{\delta}\) & \(\boldsymbol{tol}\) & **PSNR** & **Iter** \\ \hline \multirow{4}{*}{Gaussian} & & 1 & 0.0016 & 0.12 & & 0.00041 & & \(5\times 10^{-4}\) & 25.17 & 67(47) \\  & & 2 & 1.15 & 0.135 & 0.05 & 0.01 & 4.2 & \(1\times 10^{-3}\) & 24.60 & 34(9) \\  & & 3 & 1.15 & 0.135 & 0.05 & 0.01 & & \(1\times 10^{-3}\) & 25.51 & 132(8) \\  & & 4 & 0.00001 & 0.135 & & 0.02 & & \(2\times 10^{-4}\) & 25.53 & 56(10) \\  & & 5 & 0.15 & 0.14 & 0.005 & 0.008 & & \(5\times 10^{-4}\) & 25.52 & 28(13) \\ \hline \multirow{4}{*}{Average} & & 1 & 0.0016 & 0.13 & & 0.00041 & & \(5\times 10^{-4}\) & 25.24 & 58(48) \\  & & 2 & 0.75 & 0.14 & 0.095 & 0.0095 & 4.2 & \(1\times 10^{-3}\) & 24.64 & 33(9) \\  & & 3 & 0.75 & 0.14 & 0.095 & 0.0095 & & \(1\times 10^{-3}\) & 25.59 & 120(8) \\  & & 4 & 0.00001 & 0.145 & & 0.02 & & \(2\times 10^{-4}\) & 25.60 & 42(14) \\  & & 5 & 0.01 & 0.14 & 0.002 & 0.009 & & \(5\times 10^{-4}\) & 25.61 & 27(15) \\ \hline \multirow{4}{*}{Motion} & & 1 & 0.0017 & 0.22 & & 0.00049 & & \(5\times 10^{-4}\) & 28.05 & 51(36) \\  & & 2 & 0.85 & 0.23 & 0.085 & 0.002 & 1.3 & \(1\times 10^{-3}\) & 27.52 & 41(7) \\  & & 3 & 0.85 & 0.23 & 0.085 & 0.002 & & \(1\times 10^{-3}\) & 28.57 & 67(12) \\  & & 4 & 0.00001 & 0.24 & & 0.03 & & \(2\times 10^{-4}\) & 28.51 & 36(7) \\  & & 5 & 0.01 & 0.24 & 0.03 & 0.003 & & \(5\times 10^{-4}\) & 28.59 & 37(10) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numerical results for Cameraman image  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Blur** & \(\mathbf{P_{0}}\) & **Alg** & \(\boldsymbol{\alpha}\) & \(\boldsymbol{\beta}\) & \(\boldsymbol{\gamma}\) & \(\boldsymbol{\lambda}\) & \(\boldsymbol{\delta}\) & \(\boldsymbol{tol}\) & **PSNR** & **Iter** \\ \hline \multirow{4}{*}{Gaussian} & & 1 & 0.0016 & 0.17 & & 0.0004 & & \(5\times 10^{-4}\) & 26.17 & 69(48) \\  & & 2 & 1.9 & 0.17 & 0.085 & 0.01 & 6.2 & \(1\times 10^{-3}\) & 25.89 & 35(8) \\  & & 4 & 0.00001 & 0.17 & & 0.085 & 0.01 & & \(1\times 10^{-3}\) & 26.22 & 92(5) \\  & & 4 & 0.00001 & 0.17 & & 0.09 & & \(2\times 10^{-4}\) & 26. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Blur** & **P\({}_{0}\)** & **Alg** & \(\boldsymbol{\alpha}\) & \(\boldsymbol{\beta}\) & \(\boldsymbol{\gamma}\) & \(\boldsymbol{\lambda}\) & \(\boldsymbol{tol}\) & **PSNR** & **Iter** \\ \hline \multirow{4}{*}{Gaussian} & & 1 & 0.0016 & 0.12 & & 0.00041 & \(5\times 10^{-4}\) & 25.13 & 60(49) \\  & & 3 & 2.5 & 0.13 & 0.07 & 0.009 & \(1\times 10^{-3}\) & 25.17 & 58(6) \\  & & 4 & 0.00001 & 0.14 & & 0.11 & \(2\times 10^{-4}\) & 25.29 & 74(5) \\  & & 5 & 0.10 & 0.12 & 0.0003 & 0.075 & \(5\times 10^{-4}\) & 25.31 & 36(6) \\ \hline \multirow{4}{*}{Average} & & 1 & 0.0016 & 0.12 & & 0.00041 & \(5\times 10^{-4}\) & 25.19 & 54(50) \\  & & 3 & 2.4 & 0.135 & 0.075 & 0.008 & \(1\times 10^{-3}\) & 25.24 & 62(5) \\  & & 4 & 0.00001 & 0.13 & & 0.18 & \(2\times 10^{-4}\) & 25.38 & 85(5) \\  & & 5 & 0.01 & 0.130 & 0.0001 & 0.070 & \(5\times 10^{-4}\) & 25.38 & 35(7) \\ \hline \multirow{4}{*}{Motion} & & 1 & 0.0018 & 0.24 & & 0.00052 & \(5\times 10^{-4}\) & 27.70 & 54(36) \\  & & 3 & 0.6 & 0.265 & 0.09 & 0.02 & \(1\times 10^{-3}\) & 27.87 & 34(14) \\  & & 4 & 0.00001 & 0.26 & & 0.12 & \(2\times 10^{-4}\) & 27.91 & 52(5) \\  & & 5 & 0.01 & 0.255 & 0.0001 & 0.050 & \(5\times 10^{-4}\) & 27.91 & 22(4) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical results for Boat image  
Figure 1: Restored images by Algorithms 1 and 3 (The first row images are Cameramen images for Gaussian blur, the second row images are Lena images for Motion blur, the third row images are House images for Motion blur, and the fourth row images are Boat images for Average blur).