# Interpolation-Filtering Method for Image Improvement in Digital Holography
## 4 Modeling
### Modeling Results  
The proposed method uses three stages: interpolation, filtering, and backward interpolation. To get the best quality of the reconstructed image, it is necessary to select the best parameters: interpolation method, image upscaling size, and filtering method. To select the best interpolation method, the quality of the reconstructed images was evaluated as part of the proposed method. Examples of filtering results from interpolations by different methods are shown in Figure 5. The image was enlarged and reduced by a factor of 2 during interpolation. In this case, median filtering was used as a filter. Quantitative values of image quality are shown in Table 1.  
Bilinear interpolation showed the best results. This is due to the fact that all information in the new pixel of the enlarged image  
It can be seen that when the size is increased up to 2 times, the image reconstruction quality is improved by 14% (NSTD), 6% (PSNR), 18% (SSIM), and 3% (SS). Thus, augmentation by interpolation improves the quality of reconstruction compared to direct application of filtering. Increasing to larger sizes, the values of metrics stop changing and remain at the same level. At the same time, the processing speed will drop when large image sizes are used. Therefore, 2-fold upscaling can be chosen as the optimal option in terms of reconstruction quality and processing time. To test the efficiency of the filtering stage, noisy holograms of flat and 3D-scenes were generated. The following digital filters were applied to the reconstructed images: median, Wiener, Frost, Lee, NLM, and BM3D. The proposed method was also applied: the image was enlarged by a factor of 2 by bilinear interpolation, each of these digital filters was applied, and the image was interpolated to the original size. In order to find the filtering parameters to maximize the resulting quality, we varied the combinations of filter parameters over a wide range. When selecting the results for presentation, the criterion was the specified objective metrics, mainly NSTD and SSIM. The results for flat scene reconstruction are shown in Figure 7. The quality assessment is shown in Table 3.  
It can be seen that the proposed method gives a higher quality of the reconstructed images for almost all quality assessment metrics. For example, for SSIM value, the quality increase reaches 17%, and for NSTD value, 29%; at the same time, compared to one of the best modern filtering algorithms, BM3D, an increase of 5% and 2% is obtained, respectively. From the visual point of view, the quality also improves: the contribution of parasitic linear elements is reduced, and sharpness is improved. \begin{table}
\begin{tabular}{c c c c c} \hline
**Upscaling, Times** & **NSTD** & **PSNR** & **SSIM** & **CC** \\ \hline
1 & 0.216 & 18.87 & 0.459 & 0.9138 \\
1.1 & 0.198 & 20.46 & 0.513 & 0.9317 \\
1.3 & 0.191 & 20.14 & 0.534 & 0.9366 \\
1.5 & 0.190 & 19.91 & 0.541 & 0.9369 \\
1.7 & 0.194 & 20.41 & 0.526 & 0.9341 \\
1.9 & 0.191 & 20.28 & 0.537 & 0.9364 \\
2 & 0.189 & 20.09 & 0.542 & 0.9382 \\
3 & 0.189 & 20.09 & 0.54 & 0.9374 \\
4 & 0.189 & 20.24 & 0.541 & 0.9380 \\
5 & 0.189 & 19.81 & 0.543 & 0.9374 \\
6 & 0.189 & 19.50 & 0.543 & 0.9370 \\
7 & 0.189 & 19.64 & 0.543 & 0.9372 \\
8 & 0.189 & 20.16 & 0.542 & 0.9379 \\ \hline \end{tabular}
\end{table} 
Table 2: Reconstruction quality for different image upscaling levels.