## 3 Results and Discussion
### The Comparison of Lp_HOGS with Lp_LOGS
#### 3.1.1 The Gaussian Blur
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multirow{2}{*}{
\begin{tabular}{c} **Noise Level** \\ **(\%)** \\ \end{tabular} } & \multicolumn{2}{c}{**Lp\_LOGS**} & \multicolumn{3}{c}{**Lp\_HOGS**} \\ \cline{3-8}  & & **PSNR (dB)** & **SSIM** & **GMSD** & **PSNR (dB)** & **SSIM** & **GMSD** \\ \hline \multirow{3}{*}{Passerby} & 30 & 40.8630 & 0.9455 & 0.0165 & **41.1052** & **0.9511** & **0.0118** \\  & 40 & 39.8587 & 0.9397 & 0.0197 & **40.6369** & **0.9505** & **0.0139** \\  & 50 & 38.3621 & 0.9247 & 0.0310 & **39.7808** & **0.9422** & **0.0178** \\ \hline \multirow{3}{*}{Station} & 30 & 39.7670 & 0.9466 & 0.0126 & **39.9526** & 0.9504 & **0.0083** \\  & 40 & 38.8663 & 0.9413 & 0.0146 & **39.6986** & 0.9497 & **0.0104** \\  & 50 & 37.7629 & 0.9323 & 0.0177 & **38.5159** & 0.9428 & **0.0131** \\ \hline \multirow{3}{*}{Truck} & 30 & 39.6943 & 0.9472 & 0.0096 & **39.8380** & 0.9502 & **0.0080** \\  & 40 & 38.4550 & 0.9391 & 0.0122 & **39.2490** & 0.9491 & **0.0092** \\  & 50 & 36.8715 & 0.9253 & 0.0254 & **38.4970** & 0.9420 & **0.0119** \\ \hline \multirow{3}{*}{Garden} & 30 & 41.0244 & 0.9804 & 0.0115 & **41.2420** & 0.9879 & **0.0091** \\  & 40 & 40.5242 & 0.9781 & 0.0135 & **40.8009** & 0.9871 & **0.0099** \\  & 50 & 39.2265 & 0.9729 & 0.0214 & **40.0002** & 0.9850 & **0.0119** \\ \hline \multirow{3}{*}{Stairs} & 30 & 41.0574 & 0.9826 & 0.0124 & **41.4211** & 0.9898 & **0.0084** \\  & 40 & 40.1333 & 0.9801 & 0.0135 & **40.9604** & 0.9892 & **0.0096** \\  & 50 & 38.6847 & 0.9709 & 0.0273 & **40.0652** & 0.9868 & **0.0114** \\ \hline \multirow{3}{*}{Corridor} & 30 & 40.3201 & 0.9813 & 0.0128 & **40.7789** & 0.9904 & **0.0092** \\  & 40 & 39.4102 & 0.9775 & 0.0156 & **40.4021** & 0.9897 & **0.0105** \\  & 50 & 38.2169 & 0.9719 & 0.0300 & **39.6962** & 0.9872 & **0.0127** \\ \hline \multirow{3}{*}{Car} & 30 & 39.5951 & 0.9456 & 0.0129 & **39.9887** & 0.9502 & **0.0088** \\  & 40 & 38.6298 & 0.9397 & 0.0183 & **39.7841** & 0.9486 & **0.0103** \\  & 50 & 36.7113 & 0.9101 & 0.0229 & **38.5019** & 0.9409 & **0.0163** \\ \hline \multirow{3}{*}{Buildings} & 30 & 39.3587 & 0.9547 & 0.0171 & **39.8475** & 0.9606 & **0.0120** \\  & 40 & 38.6073 & 0.9487 & 0.0190 & **39.2298** & **0.9589** & **0.0145** \\  & 50 & 37.3181 & 0.9249 & 0.0345 & **38.6869** & **0.9531** & **0.0160** \\ \hline \multirow{3}{*}{Zebra crossing} & 30 & 39.9135 & 0.9868 & 0.0112 & **40.1558** & **0.9906** & **0.0099** \\  & 40 & 38.9183 & 0.9843 & 0.0137 & **39.7001** & **0.9900** & **0.0111** \\ \cline{1-1}  & 50 & 37.7372 & 0.9755 & 0.0264 & **38.7267** & 0.9879 & **0.0133** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The Lp_HOGS and Lp_LOGS deblurring effects on images with the \(7\times 7\) Gaussian blur. The optimal indicators for each condition are denoted in bold to facilitate data observation. Figure 2: The passerby image with different degrees of degradation. (**a**) The original image, (**b**) the \(7\times 7\) Gaussian blur, and (**c**) the \(7\times 7\) Gaussian blur + \(30\%\) salt-and-pepper noise. effect. However, Figure 3f retained more details. For example, the lines of the iron fence are clearer and more continuous. Overall, the visual effect of Figure 3f was closer to that of the original image, indicating that the deblurring performance of Lp_HOGS under the Gaussian blur was better than that of Lp_LOGS. Lp_HOGS also preserved more details while suppressing the staircase effect of deblurred images.