Image Denoising by Regularization on Characteristic Graphs

This paper introduces improvements to a now classical family of image denoising methods through rather minimal changes to the way derivatives are computed. In particular, we ask, and answer, the question “How much can we improve the common denoising methods by local, completely non-parametric modifications to image graphs?” We present the concept of non-parametric characteristic graph representations of images and detail two such graph constructions. Their use in image denoising is demonstrated within a regularization framework. The results are compared with those of more traditional approaches of Tikhonov, total variation and L 1 TV regularization. We show that in some denoising scenarios our methods perform more favorably in preserving intensity levels and geometric details of object boundaries. They are particularly useful for denoising images with both smooth and discontinuous intensity variations, preserving detail to the pixel level. Mathematics Subject Classification: 65D18, 68U10, 05C90

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