# Interpolation-Filtering Method for Image Improvement in Digital Holography
## 5 Experimental Validation of the Proposed Method
### Results  
The proposed method is applied to images reconstructed from registered digital holograms. For comparison, digital filters were applied to these images without a size increase. SC was used as a quality metric. The parameters of all filters were chosen to provide the best noise suppression and leave the sharpness and detail of the image at an acceptable level. The search for the best parameters was based on both speckle contrast values and overall subjective impression of the resulting quality after processing. The reconstructed image of the first scene, which is able to have a smaller scene depth before filtering, is shown in Figure 9b. The results of applying digital filters (a, c, e, g, i, k) and the proposed method (b, d, f, h, j, l) to the reconstructed images are shown in Figure 10. The SC values for all zones after filtering are given in Table 5. The values on the reconstructed image before filtering are also given. It can be seen that, on average, the proposed method provided a 4-fold quality improvement. At the same time, the quality is improved up to 1.4 times in relation to the application of filters. The results of applying the digital filters and the proposed method to the reconstructed cross-sections of the second scene are shown in Figure 11. The original cross sections are shown in Figure 9f.g. The SC values are shown in Table 6. The values from the reconstructed image before filtering are also shown. It can be seen that, on average, the proposed method provided threefold quality improvement. At the same time, the quality has also improved by 1.4 times in relation to the application of filters. Figure 10: 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. Filter and SC in zone 1 (from Table 5) are presented above each image. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Digital Filtering**} & \multicolumn{2}{c}{**The Proposed Method**} \\
**Filter** & **Zone 1** & **Zone 2** & **Zone 1** & **Zone 2** \\ \hline \multicolumn{4}{c}{Initial SC (coin in Figure 9f): 0.5317 (zone 1) and 0.5276 (zone 2)} \\ Median & 0.1963 & 0.2082 & **0.1675** & **0.1684** \\ Lee & 0.1672 & 0.1641 & **0.1593** & **0.1556** \\ BM3D & 0.3063 & 0.2766 & **0.2071** & **0.1972** \\ \multicolumn{4}{c}{Initial SC (coin in Figure 9g): 0.5450 (zone 1) and 0.5423 (zone 2)} \\ Median & 0.2266 & **0.1803** & **0.2246** & 0.1877 \\ Lee & 0.2320 & 0.2038 & **0.1998** & **0.1652** \\ BM3D & 0.2286 & 0.2037 & **0.2162** & **0.1920** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quality of reconstruction of the 2 nd scene cross-sections. The best values between standard and proposed method realization are given in the bold format. Figure 11: Reconstructed cross-sectional images of the second scene after the filter (**a**,**c**,**e**,**g**,**i**,**k**) and the proposed method (**b**,**d**,**f**,**h**,**j**,**l**). Median (**a**,**b**,**g**,**h**), Lee (**c**,**d**,**i**,**j**), and BM3D filters (**e**,**f**,**k**,**l**,**k**) were used. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Digital Filtering**} & \multicolumn{2}{c}{**The Proposed Method**} \\
**Filter** & **Zone 1** & **Zone 2** & **Zone 1** & **Zone 2** \\ \hline \multicolumn{4}{c}{Initial SC} & \multicolumn{2}{c}{0.5230 (zone 1) and 0.5429 (zone 2)} \\ Median & 0.1610 & 0.1892 & **0.1455** & **0.1730** \\ Wiener & 0.1505 & **0.1614** & **0.1409** & 0.1656 \\ Frost & 0.1315 & 0.1614 & **0.1189** & **0.1495** \\ Lee & 0.1603 & 0.1901 & **0.1416** & **0.1718** \\ NLM & 0.1280 & 0.1154 & **0.0941** & **0.1138** \\ BM3D & 0.0903 & 0.1197 & **0.0842** & **0.1190** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Quality of reconstruction of the 1 st scene cross-sections.