# Improved Image Denoising Algorithm Based on Superpixel Clustering and Sparse Representation
## 4 Experimental Results
### Quantitative Comparisons
In order to further testify the conclusions, we made a mean processing for the data results in Table 1, and showed the result in Figure 11. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Images**} & \multicolumn{5}{c}{**(f) \(\boldsymbol{\delta}=\boldsymbol{80}\)**} \\ \cline{2-6}  & **NLM** & **KSVD** & **BM3D** & **EPLL** & **SC-SR** \\ \hline \multirow{3}{*}{**Baboon**} & 20.68 & 21.40 & 21.64 & 21.68 & **21.71** \\  & 0.3379 & 0.3860 & 0.4049 & **0.4186** & 0.4137 \\  & 0.2387 & 0.2205 & 0.2224 & 0.2889 & **0.2988** \\ \hline \multirow{3}{*}{**Fingerprint**} & 17.75 & 19.55 & **22.39** & 21.12 & **22.39** \\  & 0.3781 & 0.5355 & **0.7478** & 0.6770 & 0.7347 \\  & 0.4376 & 0.4397 & 0.4699 & 0.3869 & **0.4956** \\ \hline \multirow{3}{*}{**Airplane**} & 22.05 & 24.18 & 25.54 & 25.61 & **25.63** \\  & 0.6723 & 0.6981 & 0.7453 & 0.7292 & **0.7902** \\  & 0.3280 & 0.3511 & 0.4741 & **0.5509** & 0.5399 \\ \hline \multirow{3}{*}{**Monarch**} & 22.52 & 22.52 & 23.20 & **23.42** & 23.29 \\  & 0.5569 & 0.7050 & 0.7237 & 0.7313 & **0.7553** \\  & 0.4911 & 0.6201 & 0.6733 & **0.7203** & 0.6947 \\ \hline \multirow{3}{*}{**Lena**} & 23.41 & 25.44 & 26.65 & 26.14 & **26.71** \\  & 0.6597 & 0.6846 & 0.7225 & 0.6952 & **0.7568** \\  & 0.2670 & 0.2793 & 0.3720 & **0.4114** & 0.3997 \\ \hline \multirow{3}{*}{**House**} & 22.29 & 24.80 & **26.94** & 26.22 & 26.74 \\  & 0.6442 & 0.6584 & 0.7379 & 0.7098 & **0.7669** \\  & 0.3322 & 0.3521 & 0.5329 & **0.5557** & 0.5204 \\ \hline \multirow{3}{*}{**Peppers**} & 19.78 & 22.97 & 24.12 & **24.19** & 24.06 \\  & 0.6038 & 0.6710 & 0.7006 & 0.7103 & **0.7391** \\  & 0.3690 & 0.4105 & 0.4783 & **0.5880** & 0.5396 \\ \hline \multirow{3}{*}{**Straw**} & 18.21 & 19.22 & 19.94 & 19.80 & **20.01** \\  & 0.2248 & 0.3306 & 0.4410 & 0.4210 & **0.4584** \\  & 0.3582 & 0.3758 & 0.3812 & 0.3344 & **0.4187** \\ \hline \multirow{3}{*}{**Hill**} & 22.84 & 24.66 & **25.28** & 25.19 & 25.23 \\  & 0.4993 & 0.5544 & 0.5865 & 0.5784 & **0.5967** \\  & 0.1925 & 0.2137 & 0.3179 & **0.3352** & 0.3349 \\ \hline \multirow{3}{*}{**Woman**} & 22.58 & 24.55 & **25.39** & 25.29 & 25.24 \\  & 0.5967 & 0.6279 & 0.6551 & 0.6419 & **0.6739** \\  & 0.2998 & 0.2612 & 0.3610 & **0.4118** & 0.3976 \\ \hline \multirow{3}{*}{**Average**} & 21.21 & 22.93 & 24.10 & 23.87 & **24.11** \\  & 0.5174 & 0.5852 & 0.6465 & 0.6313 & **0.6686** \\ \cline{1-1}  & 0.3314 & 0.3524 & 0.4283 & 0.4584 & **0.4640** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._In Figure 11, we demonstrated the total averages of the PSNR, SSIM and FOM for NLM, K-SVD, BM3D, EPLL and SC-SR. For each algorithm, the total average PSNR was calculated by the mean of the average PSNR results with different noise variances (Table 1), and the total average SSIM and the total average FOM were calculated in the same way. As seen in Figure 11, it was obvious that SC-SR achieved the highest total average PSNR and total average SSIM, while EPLL attained the highest total average FOM. SC-SR was close to EPLL and higher than BM3D for the total average FOM. BM3D had a similar total average PSNR as SC-SR, but a lower total average SSIM and total average FOM than SC-SR. EPLL had higher total average FOM, but lower total average PSNR and total average SSIM than SC-SR and BM3D. In brief, among the five algorithms, BM3D possessed the best capacity for removing noise and preserving structural information, and the second-best capacity for preserving edge areas. In general, SC-SR could not only effectively remove the noise, but also preserve the image edge regions and structural information in the round. All experiments were run under the MATLAB 2014a environment on a machine with Intel(R) Xeon(R) E5-2690 CPU of 2.60 GHz and 96.0 GB RAM. Owing to compiled C++ mex-function and parallelization implementation, BM3D proved to be the fastest algorithm. Furthermore, NLM benefited from compiled C++ mex-function, and turned into the second-fastest algorithm.