# Interpolation-Filtering Method for Image Improvement in Digital Holography
In this paper, we will limit the consideration of well-known and widely used non-neural network filters that require only 1-5 filtering parameters. In fact, for practical applications, even the necessity of blind selection of several parameters is an inconvenience. Also, each filter has a limitation on the processing quality for a single image. At the same time, even complex filters (e.g., NLM and BM3D) give low reconstruction quality at high noise levels, which occurs in digital holography [35; 36]. To solve this problem, this paper proposes a filtering method with interpolation. Interpolation has worked well in image quality enhancement [57; 58; 59], digital image correlation [60], magnetic resonance imaging [61], etc. In microscopy, resolution has been enhanced by physical interpolation [62], image interpolation with denoising [63], image interpolation with edge detection [64], etc. Interpolation is also used to suppress spatial structure, such as a grid appearing after JPEG compression [65]. In digital holography, interpolation of hologram image has improved the quality of reconstruction by creating a set of aliased spectra [66] and iterative reconstruction [67]. Digital hologram self-extrapolation [68] and a combination of extrapolation with hologram interpolation [69; 70; 71] iteratively improved the quality of the reconstructed images. To increase the reconstruction quality, this paper proposes a method that unifies useful features of digital holography, digital filtering, and interpolation techniques. Firstly, the image is reconstructed from the hologram. Then, this image is interpolated to a larger size. The core of optical solutions is increasing the information wherein standard realization of digital methods cannot obtain additional pixel information. In this paper, interpolation is used to increase the statistical basis of pixels and signal-to-noise ratio. Then, a digital filter is applied after increasing the image size. Thus, the filter uses more pixel information than the standard realization. The image is then interpolated to the original size. This combination allows, at the expense of the statistical pixel base, to extend the quality enhancement limit compared to the standard filter implementation. In this paper, we compare different filters used in digital holography with their versions modified according to the proposed algorithm. Among these filters are the widely used median filter, one of the most efficient NLM and BM3D filters [72], the weighted averaging filters Lee and Frost, and the well-known Wiener filter. According to our knowledge, the proposed method is the first approach in digital holography, where interpolation was used to increase the pixel statistics of the reconstructed image directly. This work is a study of a proposed multistage technique, which makes a significant contribution to the development of quality improvement methods in digital holography. Using the proposed method, a very significant increase in quality was obtained compared with unmodified methods. As a result, it opens a new direction in improving the quality of digital holograms based on the expansion of processed data statistics. The paper is organized as follows. Section 2 discusses the factors that degrade the quality of reconstruction from digital holograms and methods to improve the quality. Section 3 describes the proposed filtering method with interpolation. In Section 4, the method is numerically validated and compared with other filters. In Section 5, the proposed method is experimentally validated and compared with filters. The Conclusion describes the main conclusions and results of the work.