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    188宝金博页面版: Total Generalized Variationpock_tgv

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    内容提示： Total Generalized VariationKristian BrediesKarl KunischThomas PockMay 14, 2010AbstractThe novel concept of total generalized variation of a function uis introduced and some of its essential properties are proved. Differ-ently from the bounded variation semi-norm, the new concept involveshigher order derivatives of u. Numerical examples illustrate the highquality of this functional as a regularization term for mathematicalimaging problems. In particular this functional selectively regularizeson different re...

    文档格式：PDF | 页数：42 | 浏览次数：19 | 上传日期：2014-11-12 16:43:09 | 文档星级：
    Total Generalized VariationKristian BrediesKarl KunischThomas PockMay 14, 2010AbstractThe novel concept of total generalized variation of a function uis introduced and some of its essential properties are proved. Differ-ently from the bounded variation semi-norm, the new concept involveshigher order derivatives of u. Numerical examples illustrate the highquality of this functional as a regularization term for mathematicalimaging problems. In particular this functional selectively regularizeson different regularity levels and, as a side effect, does not lead to astaircasing effect.Keywords: Bounded variation, total generalized variation, tensor fields,regularization, image denoising.AMS Subject Classification: 49J52, 49N45, 68U10.1IntroductionMost mathematical formulations of inverse problems and in particular ofmathematical imaging problems are cast in the formminuF(u) + R(u),(1.1)where F represents the data fidelity and R the regularization term. If Gdenotes the forward modeling operator then the most common fidelity termis of the formF(u) =1where z stands for the possibly error-prone data and · denotes an ap-propriately chosen Hilbertian norm. Similarly the most frequently chosenregularization term is given by2G(u) − z2,(1.2)R(u) =α2|u|2,(1.3)where α is the regularization parameter and | · | again denotes a Hilbertiannorm or semi-norm. It is now becoming well-accepted that the mathematical1

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