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Fourth-order partial differential equations for image enhancement. (English) Zbl 1124.65096
The authors propose a method for noise removal which based on a combination of a model by F. Catté, P.-L. Lions, J.-M. Morel and T. Coll [SIAM J. Numer. Anal. 29, No. 1, 182–193 (1992; Zbl 0746.65091)] with fourth-order terms. They prove the correctness of the proposed model and show that it is numerically superior to that of P. Perona and J. Malik [Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)] Catté et al. [loc. cit.], and T. Chan, A. Marquina and P. Mulet [Second order differential functionals in total variation-based image restoration. (to appear)].

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K30 Initial value problems for higher-order parabolic equations
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
Full Text: DOI
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