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.

本文提出了一种新的图像平滑方法及其在遥感领域的应用。该方法基于笛卡尔坐标系中任意次数的迭代拉普拉斯算子的最小化。使用有限差分法，得出线性组合，该组合表示最小化问题的解决方案。对于普通Laplace运算符的特殊情况，该解决方案以9×9模板明确表示。为了展示在遥感领域的潜在应用，针对伊朗进行了一项研究。在这项研究中，Sentinel-2卫星图像用于13个波段，具有不同的几何分辨率。使用导出的模板，可以对每个频段进行全面分析。结果表明，可以在图像中检测到各种现象，包括不同土壤类型的位置。比较Laplace模板的独立方法，新提出的方法的L ₀梯度平滑，局部拉普拉斯平滑和树滤波表明，该新方法在确定卫星图像感兴趣区域中存在的各种现象时更有效。