# A Digital Denoising Method Based on Data Frequency Statistical Filtering
###### Abstract  
Noise amplitude in original time domain data is usually discrete and sparse. This article presents a digital filter denoising method based on statistical frequencies of the signal values. The effective signal and noise signal are identified by comparing the frequency of the value of each pixelin the original signal with the preset validity discrimination threshold. Signals recognized as valid will be output directly, while noise signals will be replaced by the mean value of their surrounding pixel values. Compared to classical digital filtering methods such as mean filtering and median filtering, this method may improve signal recognition accuracy and has the potential to remove random noise while retaining details. An image noise reduction software based on frequency statistics was developed in the MATLAB environment. Noise reduction based on this algorithm was implemented on a portrait image with a noise density of 5%-40%, and noise reduction efficiency was compared to the classical noise reduction algorithms. The experimental results show that the _PSNR_ of the proposed new method exceeds 41, reaching the same level as switching median filtering and adaptive filtering and preceding mean filtering. The _SSIM_ of the new method exceeds 0.97, which is better than other classical methods. Additionally, the higher the noise density, the more obvious the advantage of this method. filtering methods; frequency statistics; random value impulse noise; denoising +
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pepper noise. Its basic principle is to sort the pixel block values around the processing pixel block and replace the value of the pixel block to be processed with the median value of the arrangement. Although this method has a good filtering effect on salt and pepper noise, the operation is complicated, easily causing discontinuity in the image, and the denoising effect decreases seriously with increasing noise density. Therefore, in order to solve the defects of the median filter, many improved algorithms have been developed gradually. In 1984, [PERSON] proposed a weighted median filtering algorithm to solve the blurring problem affecting details and the edges of images caused by traditional median filters [6]. The basic principle is to re-weight the pixel blocks in the window, and the weight of each pixel block is taken as the number of the pixel blocks. The pixel block values in the window are then rearranged and the median value is taken as the value of the pixel block to be processed. This method strengthens the influence factor of pixel blocks that are close to the center block. By adjusting the weight, the image details can be better protected. However, as with the median filter, the denoising effect of this algorithm is poor when noise density is high. The essence of the median filtering method is to replace the value of the center noise pixel block with the median value of a certain arrangement of the domain pixel block; thus, it is bound to cause image blurring, and this blurring will become more serious with increases in noise density. Therefore, the degree of blur should be reduced to improve the denoising effect. In 1994, [PERSON] proposed the new idea of first detecting the noise in the images and then filtering it, and invented the switching median filtering method [7]. Its basic principle is to first detect whether the pixel block to be processed is a noise pixel block. If so, it will be processed. If not, it is kept. Subsequently, many scholars proposed various improved algorithms based on this principle [8; 9]. [PERSON] proposed the progressive switching filter [10], which makes the image locally smooth. The filtering effect is better than the switching median filter, but the disadvantage is the large amount of computation and the complexity of the algorithm. [PERSON] proposed the BPDF method [11], which greatly optimized the amount of calculation and operation efficiency; however, the denoising effect also decreased significantly with improved noise density.