# Interpolation-Filtering Method for Image Improvement in Digital Holography
## 4 Modeling
### Modeling Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Baseline Values: NSTD = 0.430, PSNR = 11.02, SSIM = 0.29, CC = 0.7065**.} \\ \hline  & \multicolumn{4}{c}{**Digital Filtering**} & \multicolumn{4}{c}{**The Proposed Method**} \\
**Filter** & **NSTD** & **PSNR** & **SSIM** & **CC** & **NSTD** & **PSNR** & **SSIM** & **CC** \\ \hline Median & 0.239 & 19.01 & 0.46 & 0.9166 & **0.185** & **19.78** & **0.54** & **0.9405** \\ Wiener & 0.210 & 19.78 & 0.47 & 0.9232 & **0.192** & **20.80** & **0.53** & **0.9406** \\ Frost & 0.190 & 16.78 & **0.51** & 0.9404 & **0.186** & **20.17** & 0.50 & **0.9435** \\ [PERSON] & 0.204 & **20.39** & 0.48 & 0.9325 & **0.190** & 20.32 & **0.54** & **0.9413** \\ NLM & **0.180** & 18.84 & 0.54 & 0.9494 & 0.181 & **20.25** & **0.55** & **0.9495** \\ BM3D & 0.179 & 20.10 & 0.54 & **0.9506** & **0.175** & **21.27** & **0.57** & 0.9505 \\ \hline \end{tabular}
\end{table} 
Table 3: Quality of reconstruction of the flat scene. The best values between standard and proposed method realization are given in the bold format. For the reconstructed 3D-scene images, Figure 8 and Table 4 show the data for filters based on three different filtering principles: median filtering, Lee filtering, and BM3D. It can be seen that even in this case, the proposed method shows better results than the standard filtering for most metrics. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Digital Filtering**} & \multicolumn{3}{c}{**The Proposed Method**} \\
**Filter** & **NSTD** & **PSNR** & **SSIM** & **CC** & **NSTD** & **PSNR** & **SSIM** & **CC** \\ \hline \hline \multicolumn{6}{c}{“Baboon”. Initial values: NSTD = 0.2828, PSNR = 10.93, SSIM = 0.389, CC = 0.6778.} \\ Median & 0.1817 & 16.65 & 0.415 & 0.7995 & **0.1492** & **19.35** & **0.545** & **0.8542** \\ Lee & 0.1557 & **19.60** & 0.470 & 0.8376 & **0.1481** & 19.36 & **0.543** & **0.8554** \\ BM3D & **0.1392** & 18.43 & 0.482 & **0.8727** & 0.1500 & **18.73** & **0.547** & 0.8533 \\ \multicolumn{6}{c}{“Peppers”. Initial values: NSTD = 0.2538, PSNR = 11.82, SSIM = 0.438, CC = 0.8244.} \\ Median & 0.1603 & 21.10 & 0.633 & 0.9565 & **0.1340** & **22.45** & **0.698** & **0.9682** \\ Lee & 0.1455 & 22.13 & 0.665 & 0.9626 & **0.1356** & **22.16** & **0.698** & **0.9675** \\ BM3D & **0.1259** & 17.55 & 0.639 & **0.9724** & 0.1365 & **20.78** & **0.693** & 0.9667 \\ \multicolumn{6}{c}{“Man”. Initial values: NSTD = 0.2519, PSNR = 13.67, SSIM = 0.502, CC = 0.8929.} \\ Median & 0.1479 & 18.08 & 0.650 & 0.9331 & **0.1210** & **20.76** & **0.729** & **0.9525** \\ Lee & 0.1285 & 20.41 & 0.701 & 0.9463 & **0.1243** & **21.32** & **0.727** & **0.9509** \\ BM3D & **0.1107** & 22.97 & 0.780 & **0.9609** & 0.1115 & **23.28** & **0.782** & 0.9608 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Quality of reconstruction of the 3D-scene cross-sections. The best values between standard and proposed method realization are given in the bold format. Figure 7: Reconstructed images of the first scene after the filter (**a**,**c**,**e**,**g**,**i**,**k**) and the proposed method (**b**,**d**,**f**,**h**,**j**,**l**). Median (**a**,**b**), Wiener (**c**,**d**), Frost (**e**,**f**), Lee (**g**,**h**), NLM (**i**,**j**), and BM3D filters (**k**,**l**) were used. Adding interpolation may be the reason for some number of artifacts. They can be caused at the boundaries of image objects or when speckles are close to each other. However, despite the high probability of artifact formation, the distortions that appear are small, and hence, their contribution to the quality of the results is negligible. This is confirmed by similar results obtained with objective quality metrics based on different principles. The increase in processing time for the presented filters compared to the standard ones is, on average, 3.3 times. This is probably not an obstacle to their use in the standard filter conditions. The increase in processing time is mainly due to the larger image size being filtered rather than interpolation operations.