Digital images, and in particular satellite images acquired by different sensors, may present defects due to many causes. Since 2013, the Landsat 7 mission has been affected by a well-known issue related to the malfunctioning of the Scan Line Corrector producing very characteristic strips of missing data in the imagery bands. Within the vast and interdisciplinary image reconstruction application field, many works have been presented in the last few decades to tackle the specific Landsat 7 gap-filling problem. This work proposes another contribution in this field presenting an original procedure based on a variational image segmentation model coupled with radiometric analysis to reconstruct damaged images acquired in a multi-temporal scenario, typical in satellite remote sensing. The key idea is to exploit some specific features of the Mumford–Shah variational model for image segmentation in order to ease the detection of homogeneous regions which will then be used to form a set of coherent data necessary for the radiometric reconstruction of damaged regions. Two reconstruction approaches are presented and applied to SLC-off Landsat 7 data. One approach is based on the well-known histogram matching transformation, the other approach is based on eigendecomposition of the bands covariance matrix and on the sampling from Gaussian distributions. The performance of the procedure is assessed by application to artificially damaged images for self-validation testing. Both of the proposed reconstruction approaches had led to remarkable results. An application to very high resolution WorldView-3 data shows how the procedure based on variational segmentation allows an effective reconstruction of images presenting a great level of geometric complexity.
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