Minimization of a Detail-Preserving Regularization Functional for Impulse Noise Removal |
| |
Authors: | Jian-Feng Cai Raymond H Chan Carmine Di Fiore |
| |
Affiliation: | (1) Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong;(2) Department of Mathematics, University of Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy;(3) Present address: Temasek Laboratories and Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Singapore |
| |
Abstract: | 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 et al. in 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 φ
α
, inherits many nice properties from φ
α
, 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 some conjugate gradient-type methods and of a recently proposed low complexity quasi-Newton algorithm. Numerical
experiments are given to illustrate the convergence and efficiency of the two methods.
|
| |
Keywords: | Image Processing Variational Method Optimization |
本文献已被 SpringerLink 等数据库收录! |
|