# Extension of p-Laplace Operator for Image Denoising

Abstract : In this work we introduce a novel operator $\displaystyle \varDelta _{(p,q)}$ as an extended family of operators that generalize the p-Laplace operator. The operator is derived with an emphasis on image processing applications, and particularly, with a focus on image denoising applications. We propose a non-linear transition function, coupling p and q, which yields a non-linear filtering scheme analogous to adaptive spatially dependent total variation and linear filtering. Well-posedness of the final parabolic PDE is established via pertubation theory and connection to classical results in functional analysis. Numerical results demonstrates the applicability of the novel operator $\displaystyle \varDelta _{(p,q)}$.
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George Baravdish, Yuanji Cheng, Olof Svensson, Freddie Åström. Extension of p-Laplace Operator for Image Denoising. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. pp.107-116, ⟨10.1007/978-3-319-55795-3_9⟩. ⟨hal-01626927⟩

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