Minimization of a Detail-Preserving Regularization Functional for Impulse Noise Removal

13 years 4 months ago

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Recently, a powerful two-phase method for restoring images corrupted with high level impulse noise has been developed. The main drawback of the method is the computational eﬃciency of the second phase which requires the minimization of a non-smooth objective functional. However, it was pointed out in [Chan, Ho, Leung, and Nikolova, Proc. ICIP 2005, pp. 125–128] that the non-smooth data-ﬁtting term in the functional can be deleted since the restoration in the second phase is applied to noisy pixels only. In this paper, we study the analytic properties of the resulting new functional F. We show that F, which is deﬁned in terms of edge-preserving potential functions ϕα, inherits many nice properties from ϕα, including the ﬁrst and second order Lipschitz continuity, strong convexity, and positive deﬁniteness of its Hessian. Moreover, we use these results to establish the convergence of optimization methods applied to F. In particular, we prove the global convergence of som...

Jian-Feng Cai, Raymond H. Chan, Carmine Di Fiore

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