A novel algorithm for removal of salt and pepper noise using continued fractions interpolation

doi:10.1016/j.sigpro.2014.03.023

Signal Processing

Volume 102, September 2014, Pages 247-255

https://doi.org/10.1016/j.sigpro.2014.03.023 Get rights and content

Highlights

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A novel continued fractions interpolation filter (CFIF) is proposed to remove salt and peppers noise. The proposed algorithm replaces median filter with continued fractions interpolation filter.
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The performance of proposed algorithm is better than the existing algorithms.
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Proposed algorithm can preserve edges of image very well while removing high density noise.
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Proposed algorithm requires neither a window nor any prior knowledge.

Abstract

We propose a novel continued fractions interpolation filter (CFIF) to remove salt and pepper noise. The proposed algorithm replaces median filter with continued fractions interpolation filter. First, noise free pixels are left unchanged, then, the weighted mean of four-direction continued fractions interpolation is computed to estimate the corrupted pixel value. Our method requires neither a window nor any prior knowledge. The proposed method also preserves edges very well while removing impulse noise. Simulation results indicate that the CFIF outperforms other filters existing in the literature.

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: $P S N R = 10 \log_{10} (\frac{255^{2}}{M S E}), M S E = \frac{\sum_{i} \sum_{j} {(f (i, j) - Y (i, j))}^{2}}{M \times N}, I E F = \frac{\sum_{i} \sum_{j} {(N (i, j) - f (i, j))}^{2}}{\sum_{i} \sum_{j} {(Y (i, j) - f (i, j))}^{2}}$ 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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View full text

A novel algorithm for removal of salt and pepper noise using continued fractions interpolation

Highlights

Abstract

Section snippets

Background

Continued fraction interpolation

Proposed method

Simulation results

Conclusion

Acknowledgment

Pattern Recognit. Lett.

Signal Process.: Image Commun.

Signal Process.

J. Approx. Theory

J. Comput. Appl. Math

Fundamentals of Nonlinear Digital Filtering

Adaptive median filter: new algorithms and results

IEEE Trans. Image Process.

A new fast and efficient decision based algorithm for removal of high density impulse noise

IEEE Signal Process. Lett.

Improved decision-based detail-preserving variational method for removal of random-valued impulse noise

IET Image Process.

Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter

IEEE Signal Process. Lett.

An efficient switching median filter based on local outlier factor

IEEE Signal Process. Lett.

A switching median filter with boundary discriminative noise detection for extremely corrupted images

IEEE Trans. Image Process.