# Multi-Color Channels Based Group Sparse Model for Image Restoration
## 4 Experimental Results
### Objective Assessment  
The proposed model in this paper is compared with 11 state-of-the-art models. These models used for comparison include SALSA [38], BPFA [4], GSR [13], NGS [39], TSLRA [40], JPG-SR [14], GSRC-NLP [27], MAR-LOW [41], HSSE [42], IR-CNN [17], and IDBP [43]. Among the comparison models, GSR [13], JPG-SR [14], GSRC-NLP [27], and HSSE [42] are based on traditional GSR or improved GSR models, which are the same type as the proposed multi-color-channels-based GSR model in this paper. In order to comprehensively evaluate the performance of the proposed model for image restoration, the proposed model is also compared with non-GSR-based image restoration models. The BPFA [4] model uses the nonparametric Bayesian dictionary learning method for image sparse representation. The SALSA [38] model proposes an algorithm belonging to the extended Lagrangian method family to deal with constrained problems. The NGS [39] model proposes a new gradient regularization framework using nonlocal similarity. The TSLRA [40] and MAR-LOW [41] are the type of low rank minimization methods. The MAR-LOW [41] combines spatial autoregression with low rank minimization methods and achieves excellent results. The IR-CNN [17] and IDBP [43] are deep-learning-based methods. Tables 1 and 2 show the PSNR values of the restoration results on different images under the four pixels missing rates of 80%, 70%, 60% and 50% of the proposed model and the comparison models. In the tables, the best results are highlighted in bold. Table 3 shows the SSIM values of the results on different images under the four pixel missing rates of the proposed model and the comparison models, and the best results are highlighted in bold. Tables 1 and 2 show the comparison results between the proposed model and the traditional models, and Table 3 shows the comparison results between the proposed model and the deep-learning-based models. In order to reduce the burden of experiments, the result data of NGS [39], TSLRA [40], and HSSE [42], provided in HSSE [42], are used here directly to avoid repetitive implementations. The experimental data of the deep learning methods IR-CNN [17] and IDBP [43] are directly from JPG-SR [14] and GSRC-NLP [27]. Figure 2: Test images. \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}{*}{80\%} & SALSA & 24.41 & 21.91 & 23.03 & 27.32 & 22.45 & 23.20 & 23.72 \\  & BPFA & 23.25 & 21.06 & 22.47 & 27.56 & 21.10 & 22.38 & 22.97 \\  & GSR & 24.57 & 26.03 & 25.50 & 31.41 & 26.01 & 25.24 & 26.46 \\  & NGS & 24.89 & 23.85 & 24.27 & 28.87 & 23.78 & 24.58 & 25.04 \\  & TSLRA & 25.49 & 25.32 & 25.15 & 30.58 & 25.21 & 25.55 & 26.22 \\  & JPG-SR & 25.40 & 26.58 & 25.55 & 31.25 & 26.29 & 25.92 & 26.83 \\  & GSRC-NLP & 25.55 & 26.78 & 26.02 & 30.51 & 26.56 & 26.17 & 26.93 \\  & MAR-LOW & 26.40 & 30.86 & 29.21 & 33.83 & 29.66 & 29.68 & 29.94 \\  & HSSE & 25.57 & 26.61 & 26.12 & 31.83 & 26.23 & 26.27 & 27.11 \\  & Proposed & **26.43** & **30.90** & **29.28** & **33.85** & **29.67** & **29.70** & **29.97** \\ \hline \multirow{8}{*}{70\%} & SALSA & 25.71 & 24.85 & 24.99 & 29.62 & 24.69 & 25.34 & 25.87 \\  & BPFA & 24.57 & 23.95 & 24.71 & 30.37 & 23.34 & 24.47 & 25.24 \\  & GSR & 26.17 & 28.92 & 27.86 & 33.54 & 28.46 & 27.89 & 28.81 \\  & NGS & 26.08 & 26.36 & 26.18 & 30.77 & 26.29 & 26.35 & 27.01 \\  & TSLRA & 26.72 & 27.76 & 27.09 & 32.64 & 27.22 & 27.32 & 28.13 \\  & JPG-SR & 26.80 & 29.24 & 27.96 & 33.40 & 28.50 & 28.24 & 29.02 \\  & GSRC-NLP & 26.98 & 29.47 & 28.20 & 33.85 & 28.71 & 28.51 & 29.29 \\  & MAR-LOW & 28.70 & 33.82 & 32.14 & 36.21 & 32.26 & 32.75 & 32.65 \\  & HSSE & 26.87 & 29.29 & 28.25 & 33.86 & 28.57 & 28.49 & 29.22 \\  & Proposed & **28.72** & **33.90** & **32.26** & **36.23** & **32.30** & **32.77** & **32.70** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PSNR values of the proposed method and some state-of-the-art methods with pixel missing rates 80% and 70%.