Application Of Wavelet Theory In Image Diffusion

In recent years, methods of the partial differential equations and wavelet image processing not only bring about a new subject for theoretical research, but also play an important role in promoting the development of image processing. It has both important theoretical values and broad prospects for development. Image denoising is one of its important applications.In this thesis, the history of the development of image processing is introduced. The basic knowledge of digital images, images of the mathematical model, as well as the effect of image processing methods of evaluation are given, partial differential equations and wavelet analysis in image processing applications are focused on. Details of multiresolution analysis and wavelet transform are presented, and Mallat tower algorithm is given, then the wavelet transform in image denoising is discussed. Several classic equations of the partial differential equations in image processing applications are also discussed: thermal diffusion equation, Perona-Malik model and Weickert anisotropic diffusion model. And then an improved model of Weickert is put forward.Repeated images iteration is needed by partial differential equations and the image is deal with as a whole in the whole course. Although edges can be saved well, images of the texture is blurred; while wavelet transform can analyze subtle changes of image, but it causes dumbbell effect. Combining with two methods, drawbacks are overcome and better effects are achieved.For noise suppression and saving detail, a nonlinear method for combining wavelet transform with nonlinear scale diffusion is proposed in processing images by using the properties of time-frequency of wavelet transform and enhancing edges of nonlinear diffuse.Finally, through simulation experiments to verify this Denoising is more valid than before in the image quality.