In this paper the problem of Synthetic Aperture Radar (SAR) and optical satellite images co-registration is considered. Because of the distinct natures of SAR and optical images, there exist huge radiometric and geometric differences between such images. As a result, the traditional registration approaches are no longer applicable in this case and it makes the registration process challenging. Mostly motivated by the crop field monitoring problem, we propose a new variational approach to the co-registration of SAR and optical images. The core idea of our approach is to involve into consideration a constrained optimization problem on the set of affine transformations for which the cost functional is the $L^p$-cross-correlation between sustainable parts of two fattened skeletons for the selectively smoothed SAR image and the luma component of an optical image, respectively.

We discuss the consistency of the proposed statement of this problem, propose the scheme for its regularization, derive the corresponding optimality system, and describe in detail the algorithm for the practical implementation of co-registration procedure. To evaluate the performance of the proposed approach, we illustrate its crucial steps with the help of several numerical experiments and real satellite images.

本文考虑了合成孔径雷达（SAR）与光学卫星图像的配准问题。由于SAR和光学图像的不同性质，这些图像之间存在巨大的辐射和几何差异。因此，传统的注册方法不再适用于这种情况，这使得注册过程具有挑战性。主要受作物田间监测问题的启发，我们提出了一种新的变分方法来共同配准 SAR 和光学图像。我们方法的核心思想是在仿射变换集上考虑一个约束优化问题，其代价函数是 ${升}^{磷}$-分别用于选择性平滑的 SAR 图像和光学图像的亮度分量的两个增肥骨架的可持续部分之间的互相关。

我们讨论了该问题提出的陈述的一致性，提出了其正则化方案，推导出相应的最优系统，并详细描述了联合注册程序的实际实现算法。为了评估所提出方法的性能，我们在几个数值实验和真实卫星图像的帮助下说明了其关键步骤。