International Journal of Computer Vision
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
SIAM Journal on Scientific Computing
Handbook of Image and Video Processing
Handbook of Image and Video Processing
On Discontinuity-Adaptive Smoothness Priors in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Global minimization of the active contour model with TV-Inpainting and two-phase denoising
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
Selective removal of impulse noise based on homogeneity level information
IEEE Transactions on Image Processing
Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization
IEEE Transactions on Image Processing
A Detection Statistic for Random-Valued Impulse Noise
IEEE Transactions on Image Processing
Adaptive median filters: new algorithms and results
IEEE Transactions on Image Processing
A new class of quasi-Newtonian methods for optimal learning in MLP-networks
IEEE Transactions on Neural Networks
Adaptive kernel-based image denoising employing semi-parametric regularization
IEEE Transactions on Image Processing
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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 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 驴. We show that 驴, which is defined in terms of edge-preserving potential functions 驴 驴 , inherits many nice properties from 驴 驴 , 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 驴. 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.