Application Of Partial Differential Equations And Wavelet Analysis In Image Denoising

It is one of the new research fields to apply the methods of wavelet analysis and partial differential equations in image processing, which not only opens up an important research field for wavelet analysis and partial differential equations, but also play an important role in image processing and signal analysis. Denoising is one of the important application aspects.Firstly, wavelets are suited for analyzing the local structures of images while partial differential equations are suited for processing images as a whole. Combining with two methods, it will overcome the drawbacks of each method and thus result in better performance.A new image denoising method based on locally Wiener filtering with thresholding and nonlinear diffusion is presented. Locally Wiener filtering with thresholding is a simple but efficient one. We use this scheme to get a cleaner image. Then, this cleaner version is used as a guide to get the edge testing function in nonlinear diffusion to reduce noise in the original image.Secondly, because wavelet transform can only extract 3 directional features of image, in this paper, a new method of image denoising algorithm via local Wiener filtering in the wavelet domain is proposed, which can extract six directional features of image. This method is based on 2-D nonseparable finite-impulse response (FIR) filters and the discrete wavelet transform.Lastly, a lot of experiments in this paper show that the two methods can perform well both from the common used objective standards and from visual.