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Images acquired by the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard Terra and Aqua exhibit strong detector striping. This artifact is common to most pushbroom scanners and affects both visual interpretation and radiometric integrity of remotely sensed data. A considerable effort has been made to remove stripe noise and reduce its impact on high-level products. Despite the variety of destriping algorithms proposed in the literature, complete removal of stripes without signal distortion is yet to be overcome. In this paper, we tackle the striping issue from a variational angle. Basic statistical assumptions used in previous techniques are replaced by a much realistic geometrical consideration on the striping unidirectional variations. The resulting algorithm is tested on Aqua and Terra MODIS data contaminated with severe stripes and is shown to provide optimal qualitative and quantitative results.