Image Denoising Model Based on Partial Differential Equation in Wavelet Transform Domain

Wavelet denoising model firstly decomposes image into high frequency and the low frequency information, and the noise characteristics are mainly concentrated in the high frequency information, but it often appears excessive image denoising phenomenon. Therefore, in order to improve the effect of image denoising, this paper proposes an image denoising model based on partial differential equations in wavelet transform domain. The partial differential equation is combined with the wavelet decomposition. According to the characteristics of the wavelet decomposition, the partial differential equation is processed in the high frequency information. The experimental results show that the model has a good effect on the peak signal to noise ratio after image denoising. Introduction In recent years, people have paid more and more attention to the problem of image denoising.At present, there are two main methods for image noise removal: one is pre-processing before imaging; the other is denoising processing after imaging. Pre-processing requires high machine hardware, so more and more image denoising studies are placed on the post-imaging process.At present, there are three types of image denoising models[2]: the first is a space-based denoising model; the second is based on the wavelet transform domain denoising model[3]; the third is based on partial differential equations denoising model [4]. Among them, the research on the latter two models is the most. The reduced entropy of the wavelet transform after processing the image is characterized by removing noise according to different resolutions, de-correlation of the signal in the wavelet domain, selecting the basis function flexibly, and selecting the characteristics of the wavelet according to different filtering criteria, thereby making it get rid of noise, which does not depend on the size and shape of the algorithm window. The diffusion filtering of partial differential equations is anisotropic, so it can be diffused in different directions and different regions of the image, and the diffusion is related to the gradient value of the image, that is determined by the local structure of the image, so it can guarantee the correctness of smoothing and the protection of the edges. Where the image gradient value changes less, a strong filtering process is adopted to achieve a smooth noise suppression effect; where the image gradient value changes more, the diffusion effect is weakened, thus preserving local information and protecting edge features. An image enhancement model based on wavelet transform and fractional differential is proposed in literature [5], which can improve the image denoising effect. However, there will be problems of excessive denoising, such as loss of detailed information of the image, blurring of the edges, and different denoising effects for different images. Literature [6] and [7] proposed an image denoising model based on partial differential equations, which can preserve the detailed information as much as possible while denoising.However, as the number of iterations increases, the gray level of the image tends to be constant, which produces a "block" effect,which affects the quality of the image. In this paper, we first analyze the scale correlation of wavelet sub-bands, then analyze the partial 2019 International Conference on Computer Information Analytics and Intelligent Systems (CIAIS 2019) Copyright © (2019) Francis Academic Press, UK DOI: 10.25236/ciais.2019. 016 76 differential equation model, construct a new diffusion function based on its functional relations, and propose a new partial differential equation of wavelet transform domain denoising model.The model uses a new diffusion function, which uses wavelet transform to separate the high-frequency and low-frequency information, and only nonlinearly spreads the high-frequency sub-bands. Therefore, not only the denoising effect but also the number of iterations can be reduced,which can avoid the "blocky" effect.The experimental results demonstrate the validity of the model. Wavelet Scale Correlation and Threshold Analysis Correlation after wavelet transform includes: intra-scale correlation, inter-scale correlation, intra-scale and inter-scale correlation[8]. The third type of correlation includes not only the coefficients in the same sub-bands, but also the parent coefficient, so the correlation of such related information is the strongest of the three.The Gaussian noise image is decomposed by three-level wavelet, and the noise distribution is statistically analyzed. It is concluded that about 96% of the noise coefficients are distributed in the outermost two layers of sub-bands, that is the high frequency information. Wavelet threshold filtering method is used for the smoothing, which can successfully separate the high and low frequency information of the image, which plays a crucial role in the subsequent operation of the image. However, at the same time, due to its limitations in the process of denoising, or the characteristics of the noise component, it is inevitable to affect its denoising effect. Partial Differential Equation Model Analysis In literature [6], the PM model of partial differential equations is proposed. The idea is to construct a “conduction coefficient” that can be changed with the local features of the image during the smoothing process.Its diffusion function is: 2 2 2 ( ) / ( ) = + g x k x k ,(where k is the threshold). Let 0 I be the initial grayscale image, and I be the grayscale image in the change, I ∇ is the gradient of a certain pixel of the image, | | I I ∇ ∇ = ζ is the unit vector in the gradient direction, η is the tangent vector with the vertical, then: