A new optimal image smoothing method based on generalized discrete iterated Laplacian minimization and its application in the analysis of earth’s surface using satellite remote sensing imagery

In this paper a new method of image smoothing and its applications in the field of remote sensing are presented. This method is based on the minimization of the iterated Laplace operator of an arbitrary degree in the Cartesian coordinate system. Using the method of finite differences, a linear combination is derived, which represents the solution of the minimization problem. For the special case of the ordinary Laplace operator, the solution is explicitly represented in a 9 × 9 template. To show the potential applications in the field of remote sensing, a study is presented for Iran. In this study, Sentinel-2 satellite imagery is used in 13 bands, with different geometric resolutions. Using the derived template, a comprehensive analysis is presented for each band. It is shown that various phenomena can be detected in the image, including location of different soil types. Comparison of the independent methods of Laplace template, L₀ gradient smoothing, local Laplacian smoothing, and tree filtering, with the newly proposed method shows that the new method is more efficient in determining the various phenomena that are present in the area of interest in the satellite imagery.