# Retinex Based Image Enhancement via General Dictionary Convolutional Sparse Coding
## 4 Experimental Result
### Objective Evaluation  
A blind image quality assessment called natural image quality evaluator (NIQE) [26] was used to evaluate the enhanced results. A lower NIQE value represents a higher image quality. Since NIQE evaluates only the naturalness of image assessment, we used another color image assessment called auto regressive-based image sharpness metric (ARISM) [27]. In Table 1, the large data SVD-CSC method had a lower score on NIQE/ARISM than the sparse coding and large data CSC methods; thus, our method is shown to have a good balance and performance. In addition, the large data SVD-CSC method has a superior or similar performance to the single image CSC, and a lower performance than the single image SVD-CSC, but without a significant difference. Therefore, through objective evaluation, we showed that the general dictionary of large data SVD-CSC method has a robust performance in most cases.  
We reconstruct the reflectance from the limited memory dictionary illustrated in Figures 5-8 to confirm the effect of SVD-CSC. The smaller the filter size of the dictionary, the more the compression rate, which adversely affects the performance when it reconstructs reflectance and subsequently, leads to bad results. Nevertheless, our proposed SVD-CSC method represents an effective objective performance indicator. In Table 2, when the filter size is \(15\times 15\), CSC and SVD-CSC express reflectance with sufficient information, and both show similar results that are good. However, when the filter size is \(5\times 5\), the performance of the CSC is greatly reduced, whereas the SVD-CSC shows similar performance to the \(11\times 11\) filter CSC. Therefore, it can be seen that the proposed SVD-CSC can be effectively applied when the compression ratio is high.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Sparse**} & \multicolumn{1}{c}{**Single Image**} & \multicolumn{1}{c}{**Single Image**} & \multicolumn{1}{c}{**Large Data**} & \multicolumn{1}{c}{**Large Data**} \\  & **Coding**[17] & **CSC**[18] & **SVD-CSC** & **CSC** & **SVD-CSC** \\ \hline \multirow{4}{*}{**NIQE**} & Figure 5 & 5.5215 & 4.7281 & 4.6913 & 4.9423 & **4.7617** \\  & Figure 6 & 7.2126 & 5.2011 & 4.8745 & 5.9401 & **5.4191** \\  & Figure 7 & 4.8099 & 3.6200 & 3.2708 & 4.0044 & **3.6144** \\  & Figure 8 & 4.9710 & 3.6874 & 3.4015 & 4.1226 & **3.6671** \\ \hline \multirow{4}{*}{**ARISM**} & Figure 5 & 4.2104 & 3.6534 & 3.6087 & 3.7988 & **3.7133** \\  & Figure 6 & 4.6012 & 3.5023 & 3.4423 & 3.8546 & **3.5511** \\ \cline{1-1}  & Figure 7 & 3.1248 & 2.7981 & 2.6559 & 2.9061 & **2.7689** \\ \cline{1-1}  & Figure 8 & 3.4180 & 2.8211 & 2.6881 & 3.0580 & **2.8338** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Objective evaluation for Retinex algorithm (11\(\times\) 11\(\times\) 100 filters).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Filter Size**} & \multicolumn{2}{c}{**5\(\times\)5\(\times\)100 Filters**} & \multicolumn{2}{c}{**11\(\times\)11\(\times\)100 Filters**} & \multicolumn{2}{c}{**15\(\times\)15\(\times\)100 Filters**} \\ \hline \multirow{2}{*}{**Method**} & **Large Data** & **Large Data** & **Large Data** & **Large Data** & **Large Data** & **Large Data** \\  & **CSC** & **SVD-CSC** & **CSC** & **SVD-CSC** & **CSC** & **SVD-CSC** \\ \hline \multirow{4}{*}{**NIQE**} & Figure 5 & 5.4092 & 5.0324 & 4.9423 & 4.7617 & 4.7252 & 4.7053 \\  & Figure 6 & 7.2085 & 6.1543 & 5.9401 & 5.4191 & 5.2118 & 5.1904 \\  & Figure 7 & 4.6962 & 4.1081 & 4.0044 & 3.6144 & 3.4139 & 3.3392 \\  & Figure 8 & 4.8696 & 4.2718 & 4.1226 & 3.6671 & 3.5627 & 3.4919 \\ \hline \multirow{4}{*}{**ARISM**} & Figure 5 & 3.9813 & 3.8085 & 3.7988 & 3.7133 & 3.6821 & 3.6226 \\  & Figure 6 & 4.5274 & 4.0021 & 3.8546 & 3.5511 & 3.5015 & 3.4920 \\ \cline{1-1}  & Figure 7 & 3.2778 & 2.9963 & 2.9061 & 2.7689 & 2.7254 & 2.7114 \\ \cline{1-1}  & Figure 8 & 3.4842 & 3.1081 & 3.0580 & 2.8338 & 2.7121 & 2.7099 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Objective evaluation by filter size.