## 4 Model Training and Discussion of the Results Obtained
### Performance Results of Module 1 (of Figure 3) for Document-Image Deblurring  
In this sub-section, we compare the performance of Module 1 with a selection of well-known deblurring methods as presented in several recent papers from the relevant literature. Most of those methods from the literature are analytical, but only two of them are involving CNN. In Figure 6, we present for illustration sample examples of deblurring results by Module 1. As we can see in these sample pictures, most of the output images have recognizable characters. However, their respective original images are not readable (by human eyes or by an OCR system). In Figure 6, image (a) is the reference input blurred image, which has been, by the way, also used in several previous related studies. We can clearly see (through a qualitative visual inspection by human eyes) in Figure 6 that Module 1 produces a better-quality output image compared to those obtained by the other competing models from previous works (the two latest of them are CNN-based). Table 2 shows the result of the ablation study. It is very clear that the base model improves while adding the new blur and Gabor filters. Figure 6: Sample results of deblurred images obtained by using our Module 1 model provided in Figure 4.  
For a further, this time \"quantitative\" testing, we now process all output images such as that in Figure 6 by a well-known OCR system called Tesseract (Figure 7 shows the output images obtained by Module 1; for the other models from the literature, the same input images are taken, and corresponding outputs are generated). Tesseract is a free, open-source OCR software. All the sample output (deblurred) images (shown in Figure 6) are tested for readability by the Tesseract OCR [73] version 5.0.0. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Considered Deblurring Models** &
\begin{tabular}{c} **Character Recognition Accuracy** \\ **(CRA) by the Tesseract OCR** \\ \end{tabular} & **Average PSNR** \\ \hline _Blurred reference images_ & 0 & 14.15 \\ \hline _Our model without blur and Gabor filters_ & 70.23 & 32.32 \\ \hline _Our model without Gabor filters_ & 81.32 & 32.76 \\ \hline _Our model without blur filters_ & 91.12 & 33.32 \\ \hline _Our model, Module 1_ & 94.55 & 33.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Showing the result of ablation study for the blur enhancement. Figure 7: Comparison with respect to blur enhancement between our model and different related models from the relevant literature. Image (**a**) shows the blurred input image; this image is used to test all models involved in this comparison. Most of those algorithms, except model (**i**), are using analytical models, but model (**i**) and our model (**j**) are using CNN. This is why these two last-named models are also improving the image’s contrast. An overview of the evaluation results obtained in this comparative testing is shown in Table 3. Indeed, a good readability by the OCR system expresses the better quality of the enhanced image (obtained from the deblurring). Finally, the output images are also compared in terms of PSNR to show the \"objective\" quality of output images. The total number of images used for testing each model for producing the results of Table 2 was 1500 images. Those images were produced based on 100 images from the image dataset of [PERSON] et al. [71]; the blur types and parameters used are defined in Table 1.  
The results presented in Table 3 above clearly show that most deblurring models result in a very large number of errors and can therefore not be used for reliably deblurring document images for a later reading by an OCR system. Although still weaker compared to that of Module 1, the only previous method with acceptable performance is the one by [PERSON] et al. [78]. The concept of that model is, however, an analytical model, and reaches a performance of 92.48% character recognition accuracy (see Table 2).