Regularization schemes involving self-similarity in imaging inverse problems

In this paper we introduce and analyze a set of regularization expressions based on self-similarity properties of images in order to address the classical inverse problem of image denoising and the ill-posed inverse problem of single-frame image zooming. The regularization expressions introduced are constructed using either the fractal image transform or the newly developed 'Nonlocal-means (NL-means) image denoising filter' of Buades et al. (2005). We exploit these regularization terms in a global MAP-based formulation and produce analytical and computational solutions. Analytical comparisions are made with results based on classical methods (e.g., fractal-based denoising and zooming, and NL-means image denoising).

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