# An Improved Image Filtering Algorithm for Mixed Noise
## 1 Introduction  
Images are inevitably affected by noise during the process of acquisition, storage, recording, and transmission, which reduces the image contrast and seriously affects the application of images [1]. For most images, the noise mainly comes from Gaussian noise and impulse noise. In many cases, the two types of noise appear at the same time. Gaussiannoise comes from electronic circuit noise and sensor noise caused by low lighting or high temperature. It has the characteristics of high density and a wide fluctuation range of noise intensity [2]. Impulse noise is also called salt and pepper noise, which is generated by the image sensor, transmission channel, decoder, etc., and appears as black and white spots on the image. In the process of image denoising, the main factor to be considered is to ensure the integrity of image features while removing noise. These features mainly include the information of image edge, image contour, image texture, and image color, etc. Traditional filtering algorithms are mainly divided into two categories: spatial domain and frequency domain [3]. The spatial domain method processes the image pixels directly, and traditional spatial filtering includes median filtering, mean filtering, Gaussian filtering, and bilateral filtering. The frequency domain method transforms the original image into the frequency domain through integral transformation, then deals with the image in the frequency domain and finally transforms it into the spatial domain inversely to enhance the image and achieve the purpose of denoising. Traditional frequency domain filtering includes Fourier transform, discrete cosine transform, wavelet transform, and multi-scale geometric analysis, etc. Among all the algorithms for removing salt and pepper noise in images, traditional median filtering is a commonly used and effective method. The algorithm uses the median value of pixels in the neighborhood of a small window to replace the gray value of each pixel in the original image, which has a good effect on suppressing impulse noise. The image edge and other details can be better maintained. The disadvantage is that the algorithm uses the neighborhood median to replace all pixels of the noise image, which makes the algorithm's filtering performance drop sharply under the condition of high-density noise pollution, and even loses its denoising performance, and the edges are prone to shift and the texture details are not clear. For this reason, some improved median filtering algorithms [4; 5; 6; 7; 8] have been proposed. These algorithms improve the performance of median filtering to a certain extent and can filter out salt and pepper noise with high density; however, the protection of image edge details is still not ideal. Reference [9] is an improved Adaptive Median Filter (AMF) algorithm, which can adjust the size of the filter window according to the noise density, but it is easy to misjudge the extreme point as a noise point to filtering. Reference [10] is another improved adaptive median filtering algorithm. Based on the idea of maximum-minimum median filtering, the algorithm uses a two-level detection method to accurately divide pixels into signal points and noise points, so as to filtering image noise effectively. Reference [11] proposed an improved multilevel median filtering algorithm (VHWR). The algorithm can better maintain the image details, greatly improve the filtering effect of salt and pepper noise with high density. However, the denoising effect is not satisfactory when the noise density is too high. Since [PERSON] et al. proposed the hard threshold function [12] and the soft threshold function [13], the wavelet threshold denoising algorithm has been widely used. However, the discontinuity of the hard threshold function will cause the reconstructed image signal to oscillate, and the fixed deviation of the soft threshold function will result in blurry or excessively smooth borders to the denoised image.