The inherent uncertainty and randomness of a random-valued impulse result in the indeterminacy and sensibility of the noise threshold. Obtaining a robust noise threshold during noise reduction is therefore difficult because of these poor features. Moreover

the noise extraction efficiencies of algorithms used for random-valued impulse reduction are seriously affected. To improve the accuracy of noise detection

this study proposes an efficient double-side impulse noise detection algorithm based on the directional characteristic and neutrosophic indeterminacy information. Given that an accurate and effective weight function is important to the performance of a filter

a new bilateral filter based on neutrosophic indeterminacy and rank-ordered absolute difference (ROAD) statistic is constructed to strengthen the weights of pixels that are similar to the current pixel and restrain the influence of pixels with high indeterminacy. For noise detection

an adaptive function of noise threshold is designed according to the relation between the performance of the peak signal-to-noise ratio (PSNR) and threshold . The value of can be automatically adjusted in this function according to the density of noise. After the values of the rank-ordered logarithmic difference (ROLD) and neutrosophic indeterminacy of each pixel are calculated

the pixels in the polluted image are divided into three types according to the relationship between the ROLD value and the threshold. The first type comprises exceeding-threshold pixels whose ROLD values are greater than or equal to threshold . The second category comprises adjacent-threshold pixels whose ROLD values are equal to or greater than 0.8 but less than . The last category comprises security pixels that have ROLD values less than 0.8 . All pixels belonging to these three types are roughly divided into noise and noise-free sets by using a switching strategy. Pixels belonging to the first type are temporarily classified as corrupted pixels because their ROLD values are greater than .All pixels belonging to the second and third types are temporarily regarded as uncorrupted pixels because their ROLD values are less than . To improve the accuracy of noise evaluation in the exceeding-and adjacent-threshold regions

different strategies are adopted to conduct a second noise examination. Pixels in the exceeding-threshold region are further detected by exploiting the directional ROLD statistics. Before the directional statistics are calculated

45°

90°

135°and 180° directional templates are designed

and different templates are applied under different noise densities. Templates with 9 pixels are used in the low-noise environment

and templates with 25 pixels are used in the high-noise condition to limit the harmful impact of noise. The smallest among the four directional ROLD values is selected as a pixel's final directional ROLD. Whether a pixel is a real noise is decided by the relationship between directional ROLD and threshold . When the selected directional statistic is less than the preset

the present pixel is firmly regarded as false noise and deleted from the noise set. Pixels in the adjacent-threshold region are re-detected by applying the statistical information of rank-ordered neutrosophic indeterminacy. When the ranking order of a pixel's neutrosophic indeterminacy is in the first three places of the filtering window

the current pixel is reclassified as noise and removed from the noise-free set. During filtering

to enhance the weights of excellent pixels that possess low indeterminacy and high similarity

a new bilateral function is built based on the ROAD statistic and neutrosophic indeterminacy. The weight of a specific pixel is jointly determined by the value of ROAD and the degree of indeterminacy information. All pixels extracted as noises are restored by applying the new bilateral function

and an iterative filtering mechanism is used for denoising to achieve a satisfactory result. Experiments show that in the exceeding-threshold region

a number of edge pixels that have been incorrectly evaluated as noises in the first checking can be extracted

and the extraction ratio of these pixels is as high as 67%. In the adjacent-threshold region

about 91% of the pixels whose statistical values are less than but close to the noise threshold can be re-extracted from noise-free set. The proposed double-side impulse noise detection algorithm not only reduces the sensitivity of the impulse noise threshold but also improves the validity of noise judgment. Under noise ratios from 10% to 80%

the proposed algorithm is compared with seven other algorithms. The new method is the best among the algorithms in terms of PSNR

mean differences in PSNR and subjective quality. The double-side impulse noise detection algorithm maximizes the use of the image directional characteristic and neutrosophic indeterminacy information during noise checking. It efficiently reduces the false rate in the exceeding-threshold region and the missed rate in the adjacent-threshold region. Therefore

many edge pixels are not damaged. The double-side detection algorithm significantly decreases the sensitivity of the noise threshold and enhances the correctness of noise detection. Furthermore

the new bilateral filter improves the accuracy of a pixel's weight by using two features to measure pixel similarity. In short

the proposed filter based on double-side impulse noise detection and a novel bilateral function fully considers uncertainty and directional information. The edges and details of the image are well protected and efficiently recovered.