# Interpolation-Filtering Method for Image Improvement in Digital Holography
## 3 Proposed Method  
### Description of the Method  
As shown in Section 2.3.3, most state-of-the-art digital filters use statistical analysis of the whole image or many pixel groups. Additional holograms are registered to increase the quantity of information. To further increase the quantity of analyzed pixels, a neighborhood of the considered pixels is processed.  
The proposed method aims to increase the statistical base of pixels. The number of pixels is increased using interpolation techniques. This is preparation for filtering and then returning the image array to its original size. The scheme of the proposed method is shown in Figure 2.  
The implementation of improved filtering using the proposed technique involves the following steps:  
1. Registration of a single digital hologram
2. Reconstructing an image of an object
3. Increase the size of the reconstructed image by interpolation
4. Applying a digital filter to an enlarged image
5. Reducing the size of the resulting image by interpolation  
In the first step, a single digital hologram of the investigated object is registered. No additional images are required to realize the proposed modification of standard digital filters.  
In the second step, the image of the registered object is reconstructed by applying a calculation of Fresnel diffraction. The region of interest of the reconstructed field containing the informative diffraction order is cropped. Further, the cropped region will be considered as the reconstructed image.  
In the third step, the reconstructed image size is increased by a factor of 2 using a bilinear interpolation. In this paper, we investigated the effectiveness of the proposed approach, depending on the interpolation method and the increase in image size. We obtained the conclusion that bilinear interpolation is more efficient than nearest-neighbor and bicubic interpolation for our application. It was also obtained that increasing the image size more than 2 times does not result in any significant increase in the efficiency of the developed method. Detailed information is provided in Section 4.2.  
In the fourth step, we apply the digital filter to the standard version. Parameters were selected for each image and filtered to obtain the best image quality after filtering. In the numerical experiment, we simply considered many combinations of parameters and chose the best one for each method according to objective quality indicators. In experiments with optically registered holograms, we relied simultaneously on speckle contrast parameters and subjective perception of the quality of the whole image.  
In the fifth step, we return the filtered image to its original size for further post-processing. Bilinear interpolation was used for image size reduction and for enlargement.  
The application of such an algorithm allows for the expansion of the capabilities of modern filters and the reduction of the influence of negative factors such as speckle noise, photosensor noise, and parasitic diffraction orders on the reconstructed image.  
Thus, the difference between the proposed method and the standard filtering is the addition of two interpolation steps before filtering--to increase the statistical basis of the pixels and the signal-to-noise ratio and after--to return the image to the original size for further processing. The first two steps are mentioned to emphasize that the reconstructed image from a single hologram is used.