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Zbl 1103.35334
Kim, Seongjai
Image denoising via diffusion modulation. (English)
[J] Int. J. Pure Appl. Math. 30, No. 1, 71-92 (2006). ISSN 1311-8080

Summary: This article studies the method of diffusion modulation, a reformulation of conventional partial differential equation (PDE)-based restoration models. The reformulated models consist of three explicit components: the diffusion operator, the modulator, and the constraint term. Strategies are suggested for their appropriate choices. In particular, the equalized net diffusion (END) and an edge-adaptive constraint term are introduced in order to successfully restore not only fine structures but also slow transitions. The new reformulated models are highly nonlinear; a linearized numerical procedure is suggested and the resulting algorithm is analyzed for stability. The reformulation has proved to outperform conventional PDE-based models in both quality and efficiency.

MSC 2000:: *35K55 Nonlinear parabolic equations
65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: variational approach; edge-adaptive constraint term; PDE-based image restoration; equalized net diffusion; linearized numerical procedure

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