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- W2066630786 abstract "In this paper, we propose a new model for image restoration and image decomposition into cartoon and texture, based on the total variation minimization of Rudin, Osher, and Fatemi [Phys. D, 60 (1992), pp. 259--268], and on oscillatory functions, which follows results of Meyer [Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, Univ. Lecture Ser. 22, AMS, Providence, RI, 2002]. This paper also continues the ideas introduced by the authors in a previous work on image decomposition models into cartoon and texture [L. Vese and S. Osher, J. Sci. Comput., to appear]. Indeed, by an alternative formulation, an initial image f is decomposed here into a cartoon part u and a texture or noise part v. The u component is modeled by a function of bounded variation, while the v component is modeled by an oscillatory function, bounded in the norm dual to $|cdot|_{H^1_0}$. After some transformation, the resulting PDE is of fourth order, envolving the Laplacian of the curvature of level lines. Finally, image decomposition, denoising, and deblurring numerical results are shown." @default.
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- W2066630786 date "2003-01-01" @default.
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- W2066630786 title "Image Decomposition and Restoration Using Total Variation Minimization and the<i>H</i><sup>1</sup>" @default.
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- W2066630786 doi "https://doi.org/10.1137/s1540345902416247" @default.
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