# Multi-Color Channels Based Group Sparse Model for Image Restoration
## 4 Experimental Results
### Objective Assessment
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Pixel Missing Rate** & **Methods** & **Bahoon** & **Butterfly** & **Girl** & **Lena** & **Mural** & **Nanna** & **Average** \\ \hline \multirow{8}{*}{60\%} & SALSA & 26.78 & 27.02 & 26.79 & 31.42 & 26.50 & 26.97 & 27.58 \\  & BPFA & 25.82 & 26.06 & 26.68 & 32.38 & 25.17 & 26.14 & 27.04 \\  & GSR & 27.74 & 31.09 & 29.54 & 35.80 & 29.98 & 30.13 & 30.71 \\  & NGS & 27.29 & 28.37 & 27.83 & 32.81 & 27.99 & 28.06 & 28.73 \\  & TSLRA & 27.92 & 29.42 & 28.91 & 34.26 & 29.07 & 29.17 & 29.79 \\  & JPG-SR & 28.14 & 31.15 & 29.87 & 35.44 & 30.15 & 30.37 & 30.85 \\  & GSRC-NLP & 28.31 & 31.46 & 30.17 & 35.95 & 30.33 & 30.59 & 31.14 \\  & MAR-LOW & 30.78 & 36.33 & 34.58 & 38.30 & 34.64 & 35.44 & 35.01 \\  & HSSE & 28.25 & 31.54 & 30.20 & 35.93 & 30.31 & 30.53 & 31.13 \\  & Proposed & **30.80** & **36.41** & **34.70** & **38.34** & **34.70** & **35.55** & **35.08** \\ \hline \multirow{8}{*}{50\%} & SALSA & 27.98 & 29.03 & 28.32 & 33.26 & 28.17 & 28.57 & 29.22 \\  & BPFA & 27.13 & 28.16 & 28.46 & 34.15 & 27.20 & 28.17 & 28.88 \\  & GSR & 29.42 & 32.78 & 31.93 & 37.64 & 31.73 & 32.16 & 32.61 \\  & NGS & 28.49 & 30.28 & 29.60 & 34.56 & 29.88 & 29.71 & 30.42 \\  & TSLRA & 29.15 & 31.01 & 30.48 & 35.52 & 30.62 & 30.87 & 31.28 \\  & JPG-SR & 29.61 & 32.83 & 31.77 & 37.18 & 31.72 & 32.21 & 32.55 \\  & GSRC-NLP & 29.75 & 33.02 & 31.95 & 37.64 & 31.88 & 32.36 & 32.77 \\  & MAR-LOW & 32.88 & 38.70 & 37.01 & 40.24 & 36.98 & 38.22 & 37.34 \\  & HSSE & 29.79 & 33.29 & 32.19 & 37.84 & 31.95 & 32.50 & 32.93 \\  & Proposed & **32.91** & **38.80** & **37.15** & **40.30** & **37.10** & **38.37** & **37.44** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PSNR values of the proposed method and some state-of-the-art methods with pixel missing rates 60% and 50%. In addition to PSNR and SSIM values of each test image, the average PSNR and SSIM values of all test images under different pixel missing rates corresponding to different models are calculated for overall comparison. It can be seen from Tables 1-3 that the proposed multi-color-channels-based GSR model in this paper obtains better results than other competitive models. Firstly, the proposed model is compared with the non-GSR-based image restoration models. In terms of the average metric values, the proposed model is 7.20 dB higher than the SALSA model, 7.77 dB higher than the BPFA model, 6.00 dB higher than the NGS model, 4.94 dB higher than the TSLRA model, and 0.06 dB higher than the MAR-LOW model. Among the GSR based models, the JPG-SR method combines the PSR model with the GSR model, and it not only preserves the advantages of the two models, but also reduces their disadvantages, and therefore the sparse representation model is unified. The GSRC-NLP method introduces group sparse residual constraints to the traditional GSR model to approximate the group sparsity of the original group and improve the quality of image restoration. The HSSR model combines the external GSR model with the internal GSR model using the NSS prior knowledge of degraded images and external data sets to optimize the image. However, the above three GSR-based-models and many other improved models not compared in this paper transform the color image into YCbCr space, and only extract the Y channel for processing. In this way, image processing cannot be loyal to each color channel of the original color image, which makes the effect of image restoration poor. The proposed method utilizes three color channels in image restoration to obtain better results, and Tables 1 and 2 prove this conclusion. Compared with the aforementioned three GSR-based models in terms of average PSNR metric values, the proposed model is 4.15 dB higher than the traditional GSR model, 3.99 dB higher than the JPG-SR model, 3.77 dB higher than the GSRC-NLP model, and 3.70 dB higher than the HSSE model.