## 4 Model Training and Discussion of the Results Obtained
### Performance Results of Module 1 (of Figure 3) for Document-Image Deblurring
Amongst all results, our model (Module 1) shows a very good and the best performance ever, which is 94.55% character recognition accuracy (CRA). Compared to the other solely CNN-based model (by [PERSON] et al. [78]) from the list of competing approaches in the benchmarking (see Table 3), our novel CNN model (Module 1) performs significantly better (Module 1: character accuracy rate of 94.55%, versus the other CNN model by [PERSON] et al. [39] having a CRA of 69.55%). Concerning PSNR, we also can see that our model is the best one, as it keeps color more in white noise and cleans the image much better. Performance Results with Regard to PSNR of Module 2 for Document-Image Noise Reduction and Contrast Improvement  
In this sub-section, we provide and briefly discuss a set of illustrative performance results of Module 2. Figure 8 shows some selected inputs and outputs of the model of Module 2. As we explained previously, contrast and noise enhancement are blindly performed jointly in the second part of our global novel model, i.e., in Module 2 of Figure 3. Indeed, Figure 8 clearly shows that contrast and noise reduction are performed simultaneously. For comprehensively measuring the performance of Module 2, we need an appropriate quality metric to better assess the efficiency of the \"noise removal + contrast enhancement\" module. For this purpose, we introduce and use a metric which was explained by [PERSON] et al. [60]. This last-mentioned source uses the peak signal-to-noise ratio, which is calculated through the explained formula (see Equation (5)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Considered Deblurring Models** & **Type of Deblurring Model** &
\begin{tabular}{c} **Character Recognition Accuracy** \\ **(CRA) by the Tesseract OCR** \\ \end{tabular} & **Average PSNR** \\ \hline _Blurred reference Images_ & - & 0 & 14.15 \\ \hline _[PERSON] and [PERSON]_[76] & Analytical & 0 & 20.12 \\ \hline _L0 deblur_[77] & Analytical & 0 & 18.14 \\ \hline _[PERSON] and [PERSON]_[78] & Analytical & 0 & 25.10 \\ \hline _[PERSON] et al._[79] & Analytical & 0 & 27.3 \\ \hline _[PERSON] et al._[16] & Analytical & 0 & 28.4 \\ \hline _[PERSON] et al._[80] & Analytical & 66.35 & 30.10 \\ \hline _[PERSON] et al._[16] & Analytical & 92.48 & 33.50 \\ \hline _[PERSON] et al._[78] & ConvNet & 68.3 & 32.20 \\ \hline _[PERSON] et al._[39] & GAN & 69.55 & 32.12 \\ \hline _Our model, Module 1_ & ConvNet & 94.55 & 33.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The character recognition accuracy (CRA) obtained for all deblurred images after testing by the Tesseract OCR software [73] version 5.0.0. Concerning noise, we compare the performance of Module 2 with some related models published in recent papers from the literature. Hereby, we consider the so-called salt noise. The models from the literature were trained mainly for salt noise, but our model is also trained and tested for Gaussian noise. Figure 9 shows the performance of our model compared to state-of-the-art models for denoising images. The original image contains peppers. One part of the peppers is zoomed in to show the sharp part of the peppers. That image is used as the original image, and a 50% noise level is added to that image. One can see how each model tries to reduce the noise level, whereby our model outperforms the other models when considering the sharpness of the respective enhanced image. Figure 8: Samples (for illustration) of removing noise from selected natural document images. Figure 9: Comparison (visual illustration of the outputs) of the performance of Module 2 for denoising with that of other denoising models from the literature. The top-left image is the original image. We use this image and add 50% noise to that image to compare the output of different denoising models. Notice that our model can also improve image contrast. Table 4 shows the PSNR performance of the different denoising models used by [PERSON] et al. [60]. The images are the same as in the source [PERSON] et al. [60] to make a comprehensive comparison possible.