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High-order total variation-based image restoration. (English) Zbl 0968.68175

Summary: The Total Variation (TV) denoising method is a PDE-based technique that preserves edges well but has the sometimes undesirable staircase effect, namely, the transformation of smooth regions ( ramps) into piecewise constant regions (stairs). We present an improved model, constructed by adding a nonlinear fourth order diffusive term to the Euler-Lagrange equations of the variational TV model. Our technique substantially reduces the staircase effect, while preserving sharp jump discontinuities (edges). We show numerical evidence of the power of resolution of this novel model with respect to the TV model in some 1D and 2D numerical examples.

MSC:

68U10 Computing methodologies for image processing
65K10 Numerical optimization and variational techniques
65F10 Iterative numerical methods for linear systems
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