# A Digital Denoising Method Based on Data Frequency Statistical Filtering
###### Abstract
[PERSON] proposed a new adaptive switching algorithm where two adaptive filters are switched correspondingly for lower and higher noise ratios. It can preserve the edges and fine details more effectively than other nonlinear filters [12]. Generally speaking, the switching median method involves two problems: (1) the noise detection method [13]; (2) the image restoration method [14; 15]. The so-called noise detection method refers to the method of dividing the pixel block into noisy pixel blocks and effective pixel blocks so that subsequent work is only carried out on the noisy pixel blocks, which achieves the purpose of protecting details. Current noise detection methods include (a) max-min noise detection [16], (b) the regression moment threshold discriminant method [17], (c) gradient threshold discrimination [18], (d) the queuing statistical discriminant method [19; 20], (e) fuzzy decision discrimination, etc. Image restoration methods also include the mean value of four fields method, the mean value of eight fields method, the median value method, etc. [21]. These methods can better avoid the destruction of non-noise point data in the filtering process, have strong edge and detail protection ability, and have a better processing effect on polluted images. However, real impulse noise does not usually have two extreme points as it does in the salt and pepper noise model, which requires another model involving random impulse noise to define it [22; 23]. The model is shown in Figure 1[24]. Its probability function is:  
\[y_{i,j}=\left\{ \begin{array}{rl}&r\;\;\;with\;probability\;,\;\;\;\;\;\;p\\ &x_{i,j}\;\;\;with\;probability\;,\;\;\;\;\;\;\;1-p\end{array} \right. \tag{1}\]  
where \(p\) is the noise level of random impulse noise and \(r\) is an integer uniformly distributed on the gray level. This kind of noise model is more realistic than salt and pepper noise, and there have been many studies on this model. Because the noise generated by random value noise is not a simple black or white dot, most of the detection algorithms for salt and pepper noise are not a pepper noise are not suitable for random value impulse noise. Especially for medium- and low-density random value impulse noise, the conventional detection algorithms miss too much. [PERSON] et al. proposed the ASMF algorithm [25], which uses the similarity measure of image pixel mean and variance to calculate the noise judgment threshold; however, the algorithm is also prone to misjudgment when noise density is high. [PERSON] proposed an improved switching median filtering method, which improved the denoising effect but also greatly increased the amount of computation and its complexity [26]. Based on the existing algorithms and the idea of probability statistics, a filtering method is proposed for the detection and filtering of medium-low density random value impulse noise. The basic principle of this method is to make use of the fact that the probability of noise points with medium and low density in the image is generally less than the probability of effective points. In this way, the noise is screened out and processed, while other effective pixels are retained. Experimental results show that the proposed method can effectively filter random impulse noise of medium and low density and retain image details and quality well. It can also adjust the denoising effect by setting various parameters, and it has the advantages of simple calculation and high operation efficiency.