# An Advanced AFWMF Model for Identifying High Random-Valued Impulse Noise for Image Processing
###### Abstract  
In this study, a novel adaptive fuzzy weighted mean filter (AFWMF) model based on the directional median technique and fuzzy inference is presented for solving the restoring high-ratio random-valued noise in image processing. This study aims, not only to obtain information from each direction of the filtering window, but also to gain information from every pixel of the filtering windows completely. Thus, in order to implement preserving details and textures for better restoration in high-noise cases, this study utilizes the directional median to build the membership function in fuzzy inference dynamically, then calculates the weighted window corresponding to the filtering window using fuzzy inference to represent the importance of valuable pixels. Finally, the restoration pixel is calculated using the weighted window and the filtering window for the weighted mean. Subsequently, this new AFWMF model significantly improves performances in the measurement of the peak signal to noise ratio (PSNR) value for preserving detail and fixed image in noise density within the range of 20-70% for the five well-known experimental images. In extensive experiments, this study also shows the better performance of identifying the proposed peak signal-to-removal noise ratio (PSRNR) and evaluating psycho-visual tests than other listed filter methods. Furthermore, the proposed AFWMF model also has a better structural similarity index measure (SSIM) value of another indicator. Conclusively, two interesting and meaning findings are identified: (1) the proposed AFWMF model is generally the best model among the 10 listed filtering methods for image processing in terms of the measurement of two quantitative indicators for both the PSNR and SSIM values; (2) different impulse noise densities should be made for different filtering methods, and thus, this is an important and interesting issue when aiming to identify an appropriate filtering model from a variety of images for processing various noise densities. fuzzy inference; weighted window; directional median; weighted mean filter; high noise 2021  
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the impulse noise from random values. The median filter replaces the filtering window's centered pixels with the filtering window's median. This filter applies a median operation for every pixel. Therefore, it modifies both undisturbed pixels and pixels with noise, and some detail which must be preserved in an image is removed [1]. Some modified median filters, such as the weighted median filter [12] and the center-weighted median filter [13], have been implemented to solve this problem. These two filters can operate effectively at low noise ratios but not at high noise ratios, since their performance in terms of spurious and missing detections is constrained [12]. This is resolved by using a switching median filter [13; 14]. This filter is mainly used for noise median filtering and detection mechanisms. A threshold is used in the detection stage to detect whether the data are tainted [12]. The filtering process is executed only if the filter contains noise. Later, various methods for reducing random-valued impulse noise were devised, such as the tri-state median filter [15], the directional weighted median filter [16], the modified switching median filter [17], the fuzzy-reasoning median filter [18], the simple adaptive median filter [19], the efficient decision-based algorithm [20], neural networks and fuzzy decisions [21], the elimination of impulse noise using an efficient algorithm [22], and threshold Boolean filtering [23], but these methods can fail at noise ratios over than 50 percent when using ranking order absolute difference [3; 4] and adaptive switching median filters [12]. The above filters apply the standard median filter at the filtering stage. In general, the median filter could be poor when used with high noise ratios of over 50%.