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On multiresolution schemes using a stencil selection procedure: applications to ENO schemes

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Abstract

This paper is devoted to multiresolution schemes that use a stencil selection procedure in order to obtain adaptation to the presence of edges in the images. Since non adapted schemes, based on a centered stencil, are less affected by the presence of texture, we propose the introduction of some weight that leads to a more frequent use of the centered stencil in regions without edges. In these regions the different stencils have similar weights and therefore the selection becomes an ill-posed problem with high risk of instabilities. In particular, numerical artifacts appear in the decompressed images. Our attention is centered in ENO schemes, but similar ideas can be developed for other multiresolution schemes. A nonlinear multiresolution scheme corresponding to a nonlinear interpolatory technique is analyzed. It is based on a modification of classical ENO schemes. As the original ENO stencil selection, our algorithm chooses the stencil within a region of smoothness of the interpolated function if the jump discontinuity is sufficiently big. The scheme is tested, allowing to compare its performances with other linear and nonlinear schemes. The algorithm gives results that are at least competitive in all the analyzed cases. The problems of the original ENO interpolation with the texture of real images seem solved in our numerical experiments. Our modified ENO multiresolution will lead to a reconstructed image free of numerical artifacts or blurred regions, obtaining similar results than WENO schemes. Similar ideas can be used in multiresolution schemes based in other stencil selection algorithms.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, Spain

    Sergio Amat, Sonia Busquier & J. Carlos Trillo

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  1. Sergio Amat
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  2. Sonia Busquier
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  3. J. Carlos Trillo
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Correspondence to Sergio Amat.

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Amat, S., Busquier, S. & Trillo, J.C. On multiresolution schemes using a stencil selection procedure: applications to ENO schemes. Numer Algor 44, 45–68 (2007). https://doi.org/10.1007/s11075-007-9083-5

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