Abstract
Improving the modeling of natural images is important to go beyond the state-of-the-art for many image processing tasks such as compression, denoising, inverse problems, and texture synthesis. Natural images are composed of intricate patterns such as regular areas, edges, junctions, oriented oscillations, and textures. Processing efficiently such a wide range of regularities requires methods that are adaptive to the geometry of the image. This adaptivity can be achieved using sparse representations in a redundant dictionary. The geometric adaptivity is important to search for efficient representations in a structured dictionary. Another way to capture this geometry is through non-local interactions between patches in the image. The resulting non-local energies can be used to perform an adaptive image restoration. This paper reviews these emerging technics and shows the interplay between sparse and non-local regularizations.
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