# An Improved Image Filtering Algorithm for Mixed Noise
## 1 Introduction
A large number of scholars have proposed many improved wavelet threshold functions to achieve a more accurate denoising effect [14; 15; 16; 17; 18; 19]. Reference [20] proposed a new wavelet threshold algorithm that overcomes the problems of fixed deviation and discontinuity in the traditional wavelet threshold function, and improves the wavelet threshold function and the threshold. Reference [21] combines the advantages of the joint regularization restoration method of spatial local threshold processing and wavelet domain processing and can achieve good results in effectively suppressing noise and artifacts. Reference [22] takes advantage of the merits of traditional Wiener filtering in the wavelet domain to deal with mixed noise, and it carries out improved Wiener filtering based on multi-directional weighting, so that the algorithm can well maintain the detailed features of the original image and further improve the peak signal-to-noise ratio of the output image. Reference [23] has studied the multi-resolution method of Haar wavelet transform for medical image denoising. It applies Haar transform to each two-dimensional image layer separately and evaluates the whole image using three-dimensional technology. This method benefits from the similarity between adjacent image layers and has a reasonable denoising effect. Reference [24] proposed a wavelet denoising method based on an unsupervised learning model. The method uses the advantages of wavelet transform and uses an unsupervised dictionary learning algorithm to create a dictionary for noise reduction, which shows very competitive denoising performance. Reference [25] presented improvements in image gap restoration through the incorporation of edge-based directional interpolation within multi-scale pyramid transforms and reconstructed two types of image edges. Reference [26] shows how to design a complex wavelet with good characteristics based on the important characteristics of dual-tree complex wavelet transform and explains a series of applications of dual-tree complex wavelet in signal and image processing. [PERSON] et al. [27] proposed the Non-local Means (NLM) denoising algorithm in 2005. By utilizing the repeatability and self-correlation within an image, the algorithm first calculates the weighted average value of the neighborhood of all pixels in the image and the neighborhood of the current pixel, then takes the average value as the Euclidean distance between the two points and assigns weights to them through the weight function. The sum of the product of the weight and all pixels is the denoised value of the current pixel. However, the NLM algorithm still has an unsatisfactory denoising effect on excessively high noise; therefore, many new algorithms have been proposed [28; 29; 30; 31; 32; 33]. Reference [34] separates noise components from image information using Principal Component Analysis (PCA), improves the accuracy of similarity measurement of NLM algorithm, and achieves a good denoising effect. Reference [35] proposes a new NLM algorithm based on similarity confirmation. The algorithm first determines the threshold according to the distance distribution between image blocks, and it then uses the reserved image blocks to realize denoising. Reference [36] designed a new similarity weight function using the residual image information in the method noise and achieved good denoising effect. Reference [37] uses an improved NLM algorithm to solve the problems of long time-consuming, unreasonable weight distribution and failure to highlight the role of central pixels when calculating the similarity between neighborhoods by Euclidean distance. The algorithm can measure the neighborhood similarity more accurately and better retain the edge and detail information of the image when removing Gaussian noise. The denoising effect of noised images is further improved. In recent years, denoising algorithms based on sparse regularization have attracted the attention of many scholars due to their characteristics of over-completeness and sparsity. [PERSON] et al.