# Research on Image Denoising in Edge Detection Based on Wavelet Transform
## 1 Introduction  
Edges are the dividing line between different regions of an image and contain a wealth of detailed information, making them the most fundamental image features. Edge detection is a widely used operation in image processing and plays a very important role in identifying and separating geometric shapes in images [1]. Edge detection is generally the process of finding the region of the graph where the gradient changes significantly and then selecting the pixel with the highest amplitude. It can also obtain the edge information of a region by searching the transfer points where the second-order derivative is zero. Generally, the edge detection operator includes the Sobel operator, Laplace operator and canny operator [1, 2]. The canny operator is a relatively complete edge detection operators, but it is affected by image noise. Therefore, it is necessary to apply appropriate filtering (denoising) processing to the image so as to eliminate the noise and retain the original edge information to the maximum extent and improve the edge detection results of the canny operator [3, 4, 5, 6, 7]. There are many methods of image denoising, such as traditional mean filtering, median filtering, Gaussian filtering and so on. Although these methods can achieve the purpose of denoising, they produce boundary blurring, edge loss and even pseudo-edge problems. Therefore, in this paper, the wavelet transform is chosen to remove as much noise as possible from the original image, while preserving the edge information and avoiding the problems caused by other denoising methods. The wavelet transform inherits and develops the idea of the short-time Fourier transform and solves the defect that the scale of the information window does not change with frequency, so that the characteristics of certain aspects of the information can be fully highlighted. The wavelet transform is widely used in signal analysis and image processing due to its multi-resolution, low entropy and decoupling properties. [PERSON], [PERSON] et al. [8] improved the traditional thresholding method by calculating the edge information and obtained a better noise reduction effect. They improved the threshold for zeroing the wavelet coefficients in non-edge regions while preserving the image edges. [PERSON], [PERSON] et al. [9] denoised phonocardiogram (PCG) signals using different families of discrete wavelet transforms, thresholding types and techniques, and number of signal decomposition levels, and discussed the effect of the chosen wavelet function and number of wavelet decomposition levels on the efficiency of the denoising algorithm. [PERSON] et al. [10] proposed a new iterative algorithm to reduce the scattering noise in SAR images and to preserve the edges and structure of the image by aggregating the smooth wavelet transform (SWT), bilateral filtering, Bayesian estimation and anisotropic diffusion (AD) filtering. In addition, neural networks have begun to be used for image denoising. [PERSON] et al. [11; 12] used a method based on wavelet transform and deep networks image classification to improve the classification accuracy of topographic images. [PERSON] [13] used a backpropagation algorithm for training in MLP-ANN to achieve good denoising of images without prior knowledge of the degradation model. This demonstrates the promising application of neural networks in the field of denoising, which is well worth the attention of researchers. In this paper, we want to detect the edges of bridge images that were taken by UAV and obtain the relevant edge detail information. To achieve a better detection effect, wavelet transform is used in advance to remove the noise interference in the image. In the wavelet transform process, relevant comparisons and discussions of wavelet functions and the number of decomposition levels are carried out for the image decomposition, and then, the optimal choice is determined.