Fast communicationDecision-based non-local means filter for removing impulse noise from digital images
Introduction
Images are often corrupted by impulse noise in the process of transmission over noisy communication channels or recording by noisy sensors [1]. The median filter has been widely used for removing impulse noise because of its superior performance in noise suppression and edge preservation in comparison with the linear filters. However, the standard median (MED) filter is implemented uniformly across the entire image without taking account of whether a pixel is corrupted or not. Inevitably, the MED filter will modify both noise pixels and undisturbed good pixels, thus resulting in blurring or loss of image details and edges.
To prevent the alteration of undisturbed pixels, switching-based filters have been proposed. In the switching filtering scheme, the noise detector is first used to classify the pixels in the images as noise pixels and noise-free pixels and then filtering is activated for the detected noise pixels. Among the recently proposed switching-based filters are difference-type noise detection based cost function-type filter [2], second-order difference analysis based median filter [3], global–local noise detection-based adaptive median (GLAM) filter [4], switching median filter with boundary discriminative noise detection (BDND) [5], opening closing sequence (OCS) filter [6], fast switching median (FSM) filter [7], efficient edge-preserving (EEP) filter [8], switching adaptive weighted mean (SAWM) filter [9], convolutional noise detection-based switching median (CNDSM) filter [10], noise adaptive fuzzy switching median (NAFSM) filter [11] and switching-based filter using nonmonotone adaptive gradient method (NAGM) [12]. Although these switching-based filters perform better than the MED filter due to the adoption of noise detection mechanism, they only use the local statistics within a small neighborhood of pixels for image denoising and thus tend to damage image details at high noise ratios.
The non-local means (NLM) filter, recently proposed by Buades [13], replaces the considered pixel by the weighted mean of all the pixels in the whole image or the surrounding neighborhoods. This filter can preserve image details better than the point-wise filters in that it relies on the global self-redundancy of the images and measures the similarity between two pixels by evaluating the Gaussian weighted Euclidean distance between two image patches surrounding these pixels. Although the NLM filter has been widely used for removing Gaussian noise [14], [15], speckle noise [16], Rician noise [17], [18] and Poisson noise [19] in the images, it performs badly in suppressing impulse noise which follows the long-tailed non-Gaussian distribution.
To fully utilize the advantage of the NLM filter in preserving image details and overcome its drawback in removing impulse noise, the decision-based non-local means (DNLM) filter is proposed in this paper. The DNLM filter combines this local statistics based noise detector with the reference image-based non-local means filter to remove impulse noise. The proposed filter can restore the images corrupted by impulse noise effectively and it outperforms many well-known switching-based filters in terms of noise reduction and detail preservation.
This paper is organized as follows: Section 2 presents the local statistics based noise detector and the reference image based non-local means filter. Comparisons of denoised results on the standard test images and real images are made in Section 3. Finally, a brief conclusion is given in Section 4.
Section snippets
The DNLM filter
The framework of the DNLM filter is shown in Fig. 1. In the proposed filter, the local statistics based noise detector is first adopted to classify the pixels in the corrupted images as noise pixels and noise-free pixels. The noise pixels are processed by the weighted mean filter while the identity filter is applied to noise-free pixels, which will produce the reference image. Based on the noise detection results and the reference image, the non-local means filter is adopted to restore the
Simulation on standard test images
In this section, 512×512 gray-level images such as Lena, Mandrill, Goldhill, Boat and Barbara and Bridge are used as test images. The salt-and-pepper noise with uniform distribution is added to these images, which means that the pixel has equal probability of being corrupted by either a positive impulse (with value 255) or a negative impulse (with value 0). Simulations are conducted on test images corrupted by salt-and-pepper noise with the noise ratio varying from 10% to 80%. The noise
Conclusion
In this paper, we have presented a novel decision-based non-local means filter for impulse noise removal. The proposed filter realizes noisy image restoration by identifying the corrupted pixels using the local statistics based noise detector and removing them using the distinctive reference image based non-local means filter, which computes the similarity between two pixels by the piecewise weight function with the adaptive decay parameters. Comparisons of restoration performance among the
Acknowledgments
We would like to thank professor Iuri Frosio from University of Milan in Italy to provide us with the panoramic and cephalometric radiographs. This work was partly supported by Major Program of National Natural Science Foundation of China (Grant No.: 51035002), National Natural Science Foundation of China (Grant No.: 30911120497), the National 973 project (Grant No.: 2011CB933103) and the Project of the National 12th-Five Year Research Program of China (Grant No.: 2012BAI13B02).
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