کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4639293 1632050 2013 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Split Bregman iteration and infinity Laplacian for image decomposition
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Split Bregman iteration and infinity Laplacian for image decomposition
چکیده انگلیسی

In this paper, we address the issue of decomposing a given real-textured image into a cartoon/geometric part and an oscillatory/texture part. The cartoon component is modeled by a function of bounded variation, while, motivated by the works of Meyer [Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, vol. 22 of University Lecture Series, AMS, 2001], we propose to model the oscillating component vv by a function of the space GG of oscillating functions, which is, in some sense, the dual space of BV(Ω)BV(Ω). To overcome the issue related to the definition of the GG-norm, we introduce auxiliary variables that naturally emerge from the Helmholtz–Hodge decomposition for smooth fields, which yields to the minimization of the L∞L∞-norm of the gradients of the new unknowns. This constrained minimization problem is transformed into a series of unconstrained problems by means of Bregman Iteration. We prove the existence of minimizers for the involved subproblems. Then a gradient descent method is selected to solve each subproblem, becoming related, in the case of the auxiliary functions, to the infinity Laplacian. Existence/Uniqueness as well as regularity results of the viscosity solutions of the PDE introduced are proved.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 240, 1 March 2013, Pages 99–110
نویسندگان
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