@Article{JCM-22-2,
author = {Raymond, H., Chan and Ho, Chung-Wa and Nikolova, Mila},
title = {Convergence of Newton's Method for a Minimization Problem in Impulse Noise Removal},
journal = {Journal of Computational Mathematics},
year = {2004},
volume = {22},
number = {2},
pages = {168--177},
abstract = {<p style="text-align: justify;">Recently, two-phase schemes for removing salt-and-pepper and random-valued impulse noise are proposed in [6, 7]. The first phase uses decision-based median filters to locate those pixels which are likely to be corrupted by noise (noise candidates). In the second phase, these noise candidates are restored using a detail-preserving regularization method which allows edges and noise-free pixels to be preserved. As shown in [18], this phase is equivalent to solving a one-dimensional nonlinear equation for each noise candidate. One can solve these equations by using Newton&#39;s method. However, because of the edge-preserving term, the domain of convergence of Newton&#39;s method will be very narrow. In this paper, we determine the initial guesses for these equations such that Newton&#39;s method will always converge.</p>},
issn = {1991-7139},
doi = {https://doi.org/2004-JCM-8853},
url = {https://global-sci.com/article/85202/convergence-of-newtons-method-for-a-minimization-problem-in-impulse-noise-removal}
}