Image Denoising Based On Shear Wave Transform

Image denoising has always been one of the hot topics in the field of digital image processing.Among the processing of image noise,White Gaussian Noise is one of the common types of noise.In view of this kind of noise,the Wavelet ransform denoising method can be regarded as an effective denoising algorithm.This paper systematically studies the relevant theoretical knowledge of Wavelet Transform,and understands that Wavelet Transform is a good time-frequency analysis method.However,as the research progressed,it was found that when the Wavelet Transform was applied to a two-dimensional image,there were some defects in the representation of the image.Aiming at the shortcomings of Wavelet Transform in two-dimensional image application,namely the lack of representation of coefficient sparsity and image direction detail,a new Multiscale Geometric Analysis based on transform domain is proposed—Shearlet Transform.In this paper,we deeply studied the theoretical knowledge of the new image representation method of Shearlet Transform,and found that the Shearlet Transform has good anisotropy,multi-resolution and multi-scale characteristics,which can detect and locate all zero-single differences,and can carry on sparse representation of a singularity,adaptively track the direction of the singular curve.In this paper,the excellent characteristics of Shearlet Transform,combined with threshold denoising algorithm and Bilateral Filtering algorithm are used to denoise the image,and the following aspects are studied:(1)By studying the relevant theoretical knowledge of Shearlet Transform,it is found that when the multi-scale decomposition of images is realized by Laplacian Pyramid algorithm,the pseudo-Gibbs effect may occur.To solve this problem,Non-subsampled Pyramid algorithm is used to perform multi-scale decomposition of images.At the same time,the singularity,anisotropy of Shearlet Transform and the directional performance of horizontal cone and vertical cone at different scales are analyzed in the form of experimental simulation.(2)Natural images generally contain rich directional detail information,but Gaussian White Noise is isotropic.Even after transformation using mathematicaltools,it is still isotropic in the transform domain.Therefore,an image threshold denoising method based on Shearlet Transform is proposed,and compared with the Wavelet Transform image threshold denoising algorithm,the denoising effect is compared from two aspects: PSNR and Time consumed by denoising.Experimental results show that the threshold image denoising algorithm based on Shearlet Transform can achieve better denoising effect.(3)The Bilateral Filtering algorithm has a good maintenance effect on the image edges.However,due to the combination of the spatial filtering function and the gray filtering function,the operation of the Bilateral Filtering algorithm is time-consuming.The improved cosine function approximates the Gaussian kernel function and improves the operation efficiency of Bilateral Filtering algorithm.Combining the Shearlet Transform threshold denoising with the improved Bilateral Filtering algorithm,the denoising effect is compared from the PSNR and the MSE.The experimental results show that the algorithm has good denoising effect under strong noise background.