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

TL;DR

This paper introduces a novel application of multivariate sampling Kantorovich operators combined with a Down-Up scaling approach for effective gap filling and speckle noise reduction in remote sensing images, validated through numerical tests.

Contribution

The paper develops new SK-based algorithms for image reconstruction, including a multidimensional linear prediction method and a Down-Up scaling approach for noise reduction, with theoretical error estimates and convergence analysis.

Findings

Effective gap filling with the LP-SK algorithm.

Significant noise reduction demonstrated on SAR images.

Improved similarity metrics compared to existing methods.

Abstract

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, under weak 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.