标题： 采样 Kantorovich 算子在遥感图像去斑噪声中的降噪：基于 Down-Up 缩放方法和空洞填充技术 显示英文标题

标题： Sampling Kantorovich operators for speckle noise reduction using a Down-Up scaling approach and gap filling in remote sensing images

摘要： 在文献中，已经提出了几种用于恢复和增强遥感图像的方法，包括基于插值、滤波和深度学习的方法。 本文研究了多变量采样坎托罗维奇（SK）算子在图像重建中的应用，特别关注空洞填充和斑点噪声减少。 为了理解所提出算法的精度性能，我们首先利用欧拉-麦克劳林求和公式，在$C(\R^n)$中推导出一个关于逼近误差的定量估计，这在最小正则性条件下提供了更尖锐的误差界。 我们还建立了关于连续SSIM测度的差异指数的收敛结果和定量估计，适用于勒贝格空间中的函数。 此外，我们证明了一个多维线性预测结果，该结果被用来设计一个新的基于SK的重建算法来处理缺失数据，我们称之为LP-SK算法。 为了解决斑点噪声问题，我们将SK算子集成到新提出的Down-Up缩放方法中。 数值测试是在合成和真实SAR图像上进行的，以验证所提出的方法。 性能通过诸如SSIM和PSNR之类的相似性度量以及特定于斑点的指标进行评估。 与最先进的技术相比分析表明，所提出的方法的有效性。 显示英文摘要

摘要： In the literature, several approaches have been proposed for restoring and enhancing remote sensing images, including methods based on interpolation, filtering, and deep learning. In this paper, we investigate the application of multivariate sampling Kantorovich (SK) operators for image reconstruction, with a particular focus on gap filling and speckle noise reduction. To understand the accuracy performances of the proposed algorithms, we first derive a quantitative estimate in $C(\R^n)$ for the error of approximation using the Euler-Maclaurin summation formula, which provides sharper error bounds under minimal regularity conditions. We also establish a convergence result and a quantitative estimate with respect to the dissimilarity index measured by the continuous SSIM for functions in Lebesgue spaces. Additionally, we prove a multidimensional linear prediction result, which is used to design a new SK-based reconstruction algorithm to handle missing data, that we call LP-SK algorithm. To address speckle noise, we integrate SK operators into a newly proposed Down-Up scaling approach. Numerical tests are presented on synthetic and real SAR images to validate the proposed methods. Performance is assessed using similarity metrics such as SSIM and PSNR, along with speckle-specific indexes. Comparative analysis with state-of-the-art techniques highlights the effectiveness of the proposed approaches.