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In this paper, the inverse gradient operators are considered that allow for calculating the original image from its gradients, such as gradients in the horizontal and vertical directions. Different gradient operators are considered and the image reconstruction from the gradients is presented. The presented method of image reconstruction is also applied for mean operators. Examples with images processed by different gradients are given.
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Artyom M. Grigoryan, Sos S. Agaian, "Gradients, means, and image reconstruction," Proc. SPIE 11399, Mobile Multimedia/Image Processing, Security, and Applications 2020, 113990N (21 April 2020); https://doi.org/10.1117/12.2557821