# Retinex Based Image Enhancement via General Dictionary Convolutional Sparse Coding
## 4 Experimental Result
### Real Image
Additionally, we examine the effect of SVD-CSC by reconstructing the reflectance from a dictionary of limited memory. For this purpose, we compare the results when the allowable memory is altered by changing the size of the filter. If the size of the filter is reduced, the elements constituting the dictionary are reduced. Consequently, each filter compresses and expresses information more clearly than when the filter size is large, and when reconstructing reflectance from such information, each filter must have more important information such as the basis of SVD than the preceding one to obtain better reconstruction results. In Figure 9a, it is seen that when using \(5\times 5\times 100\) filters, the large data CSC does not express the local reflectance well.Meanwhile, the large data SVD-CSC in Figure 9b does not express perfect local reflectance, but it shows better results than the large data CSC. When using \(15\times 15\times 100\) filters in Figure 9c,d, both large data CSC and large data SVD-CSC have sufficient information, and hence, they show similar results. Therefore, the proposed large data SVD-CSC method can achieve better reconstruction results by constructing a compact dictionary with limited memory. Figure 6: Comparison of SVD-CSC and CSC methods without SVD: (**a**) Original test image; (**b**) Reflectance using CSC general dictionary; (**c**) Image enhancement using CSC general dictionary; (**d**) Reflectance using SVD-CSC general dictionary; (**e**) Image enhancement using SVD-CSC general dictionary. Figure 8: Comparison of SVD-CSC and CSC methods without SVD: (**a**) Original test image; (**b**) Reflectance using CSC general dictionary; (**c**) Image enhancement image using CSC general dictionary; (**d**) Reflectance using SVD-CSC general dictionary; (**e**) Image enhancement image using SVD-CSC general dictionary. Figure 7: Comparison of SVD-CSC and CSC methods without SVD: (**a**) Original test image; (**b**) Reflectance using CSC general dictionary; (**c**) Image enhancement using CSC general dictionary; (**d**) Reflectance using SVD-CSC general dictionary; (**e**) Image enhancement using SVD-CSC general dictionary. In Figures 5-8, we show the image enhancement effect in low-light image. Finally, we show that high quality reflectance images can be obtained by removing a halo artifact from image reconstruction. A common problem with Retinex-based algorithms is the appearance of a halo artifact around the high-contrast areas owing to the rapid change in illumination. The halo artifact are shown in the red box in Figure 10. As shown in Figure 10c, the halo artifact usually appear due to the smoothness conditions of illumination of the Retinex model [16]. However, in Figure 10e our proposed method can reduce this artifact because the reflectance can be reconstructed in more detail. Therefore, our proposed method can reduce a halo artifact while using limited memory in these reconstruction applications, and acquire high quality images with enhanced edges and texture such as super resolution. Figure 10: Comparison of high contrast image reconstruction: (**a**) Original test image; (**b**) Reflectance using [16] Retinex model; (**c**) Image enhancement image using [16] Retinex model; (**d**) Reflectance using SVD-CSC general dictionary; (**e**) Image enhancement image using SVD-CSC general dictionary.