A novel algorithm for removal of salt and pepper noise using continued fractions interpolation
Section snippets
Background
Images are often corrupted by salt and pepper noise in the process of image transmission. Salt and pepper noise is essentially a special case of impulse noise, where a certain percentage of pixels are randomly digitized into two extremes since impulse value normally is larger compared with the strength of the image. Many methods have already been presented to solve this problem. The well known method is to use standard median filter (SMF) [1]. The greatest shortcoming of SMF is that it is only
Continued fraction interpolation
It is difficult to get adequate noise free pixels in vicinity of corrupted pixels when the image is corrupted by high density salt and pepper noise so that neighbor interpolation effect is poor. In order to obtain better effect, median filter (neighbor interpolation) should be replaced by a better interpolation method. Thiele׳s continued fractions interpolation may be the favored nonlinear interpolation [22], [23], [24], [25], [26] in the sense that it is constructed by means of the inverse
Proposed method
In median filter, the window and window size must be given in advance according to the noise density, then the corrupted pixel value is replaced by only one pixel value in window. But in the proposed method, no window is required and our method can automatically select some noise free pixels to restore corrupted pixels. It is possible that selected pixels are far away from the corrupted pixel. Furthermore, the proposed method uses the values of all selected pixels to estimate the corrupted
Simulation results
In this section, the performance of our algorithm is tested with different grayscale images whose dynamic ranges are [0, 255]. In the simulations, 255 represents “salt” noise and “0” represents the “pepper” noise with equal probability. Performances of different algorithms are quantitatively evaluated by the PSNR and IEF, which are defined as follows:where MSE is the mean square error, IEF is the image
Conclusion
In this paper, a novel algorithm based on continued fractions interpolation for removing salt and peppers noise is presented. It first computes continued fractions interpolation in four-direction, then a weighted mean of four-direction interpolation is assigned to corrupted pixel. The proposed method does not need any prior knowledge. Experiments indicate that our method performs much better than other existing methods in terms of both quantitative evaluation and visual quality. Particularly it
Acknowledgment
This work is supported by the NSFC-Guangdong Joint Foundation (Key Project) under Grant no. U1135003 and the National Natural Science Foundation of China under Grant no. 61070227.
The authors thank the anonymous reviewers for their valuable comments, which help to improve the quality of this paper.
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2020, Computer CommunicationsCitation Excerpt :These algorithms exhibited fading effect. Interpolation techniques such as continued fractions [15], Spline [16], radial bias function [17], Kriging [18], inverse distance weighted [19] were employed for the elimination of outliers. These algorithms require adaptive window or complex calculations for evaluation of restored pixel.
An adaptive decision based kriging interpolation algorithm for the removal of high density salt and pepper noise in images
2018, Computers and Electrical EngineeringCitation Excerpt :First stage filter was a decision based median filter and second stage was unsymmetrical trimmed median [20] or midpoint [19,20] or variants [21]. Interpolation techniques such as continued fractions [24], third and fourth order Bspline [22,23], ordinary Kriging [26] were used for the removal of salt and pepper noise. These algorithm works well at very high noise densities but blotching of regions or smearing of edges takes place at high noise densities.
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2018, Journal of Visual Communication and Image RepresentationCitation Excerpt :Then the noisy-pixel's intensity is found through inverse distance weighted mean of corresponding directional estimated values and their directional criteria. In our experimental tests, to show the effectiveness and efficiency of our proposed post-processing method we adopt this method after restoration unit of some state-of-the-art DBFs such as MDWM [5], IBDND [6], RAMF [7], ASWM [8], SMMF1 [9], SMMF2 [9], IBINR [10], AWMF [11], CFIF [12], UWMF [13], NRWII [14], TSAR [15], DNLM [16], INLM [17], MASF [18], EEPARS [19], three-values-weighted approach (TVWA) [20], context-based prediction filtering (CBPF) [21], and probabilistic decision based filter (PDBF) [22]. The restoration unit of these DBFs are based on linear filters such as mean filters, rank ordered filters like different types of median filters, partial differential approaches, finite element, numerical interpolation, non-local-mean based methods and image inpainting [5–22].