## 2 Proposed Method
### Demonstration of Execution Steps of the Proposed Method  
Figure 4 demonstrates the execution steps for the proposed method. Step 1: The modules are selected from the graphic user interface. In the training phase, there is global face model learning and local geometric co-occurrence model learning. Here, two modules can be selected. The first module is the training phase, and the second module is the testing phase. Figure 5 illustrates the GUI (Graphical User Interface) of Module Selection. Step 2: Selection of training phase, the second page opens, which is the GUI of the Training Phase, which contains global face model learning and local geometric co-occurrence model learning. Figure 6 demonstrates the GUI of the training phase. Step 3: Selection of the global face model learning. Two directories can be chosen as the high-resolution directory, and they create the dictionary. Figure 7 illustrates the GUI of the global face model learning phase. Step 4: Choosing a directory for training the GUI for every image. Three poses are created so that it will be easy to compare the images with the testing phase. Figure 8 illustrates the GUI for directory selection. Step 5: All images with different misalignment variations are selected to compose a dictionary. This output shows that the dictionaries are created for each directory using online dictionary learning. Figure 9 demonstrates the GUI of the HR face sparse representation dictionary. Step 6: Steps in local geometric co-occurrence model learning. The first step chooses the LR images and extracts features from the LR patches, and the second step chooses the HR images and extracts the features of the HR patches. Figure 10 illustrates the GUI of global face model learning. Step 7: The given global face input image is divided into LR (Low resolution) and HR (High Resolution) patches that include individual parts such as the eye and nose region. Figure 11 demonstrates the selection of the LR image. Figure 12 illustrates feature extraction from the LR image. Figure 13 demonstrates the selection of the HR image. Figure 14 illustrates feature extraction from the HR Image. Step 8: On extraction of the HR and LR features from the input image, visual words are created for both the LR and HR, separately. Figure 15 demonstrates the creation of visual words. Step 9: Applying linear regression to the HR and LR visual words, the regression coefficients are determined. The regression coefficients are calculated by finding the mean value of the RGB (Red-Green-Blue) of the HR and LR image gradient features. Figure 16 demonstrates the application of linear regression on visual words. Figure 4: Execution steps of the proposed method. Figure 5: GUI of Module Selection. Figure 6: GUI of the training phase. Figure 7: GUI of global model learning. Figure 8: GUI of directory selection. Figure 10: GUI of global face model learning. Figure 9: GUI of the high-resolution (HR) face sparse representation dictionary. Figure 11: Selection of the low-resolution (LR) image. Figure 12: Feature extraction from the (LR) image. Figure 13: Selection of the HR image. **Testing Phase:**  
**Step 1**: Choosing an LR Image. Figure 17 demonstrates choosing the LR image from the directory. **Step 2**: The LR image should be applied for initialization by interpolation for resizing the LR image, which is easy to compute using the global face model. Figure 18 demonstrates initialization for interpolation. Figure 19 illustrates applying interpolation. After applying the initialization, the same  
Figure 5:0 Linear regression on visual words. Figure 5:1 Feature extraction from the (HR) image. Figure 5:2 Creation of visual words. The input LR image is initialized, and then the E-step is applied. In this step, the LR image is given as the input and it is initialized by interpolation. The image is compared to the global face image, and then it is processed to the M-step. Hence, the initialized image is compared to the local geometric co-occurrence model image, and that image is processed to the E-Step.