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Abstract
In order to increase the performance of computational algorithms in terms of efficiency of estimators, we tested new nonparametric estimators in fuzzy and cellular automata models. In particular, image de-noising algorithms exist to restore digital images corrupted by impulse noise. These algorithms may do poorly in many common cases, for example, when high contrast and sharp edges lead to outliers, spikes, or non-symmetric patterns for neighborhing pixels. This would stem from the choices of estimators in the algorithms. We investigated new nonparametric estimators and compared to existing methods in simulation study. We detected better performances of our new methods under various situations.
Highlights
Noise filtering is an important aspect of image processing
In particular we considered the median and Hodges-Lehman estimator (HL) for measures of centrality, and the interquartile range (IQR), median absolute deviation (MAD), and dispersion type (Disp) for measures of spread
We can see that for ratios less than 50% the modifications (G 3-2), (G 4-2), and (G 4-4) all outperform the original by 0.5-1 which increased the efficiency of the estimators from 12% to 26%
Summary
Noise filtering is an important aspect of image processing. It has the obvious aesthetic justification of representing clear and precise images and a practical one in the age of machine learning and computer vision where supervised learning algorithms rely on accurate and uncorrupted sources to train on. The particular type considered here is salt & pepper noise, where pixel values are corrupted randomly to either the maximum or minimum intensity, which, in the black and white case, corresponds to uniformly, distributed black and white dots. Many algorithms exist to filter salt & pepper noise, in this paper we consider an existing fuzzy cellular-automata filtering algorithm and test the performance of nonparametric estimators using distributional properties in place of center and spread statistics that rely on more assumptions than might be realistic
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