PDE Based Image Denoising

Image is the most important means for people to understand the world clearly. During the digital image processing, image signal is contaminated inevitably by noisy signal due to limitation of imaging methodology and external disturbance. It is necessary for digital image to be preprocessed before being used for analysis because the edge and minutia in noise may lead to difficulty in the following image process, such as edge detection, image segmentation and image registration. Image denoising is one of the most popular technologies in dealing with image processing. It mainly uses the features that noise and signal distribute differently in the frequency domain. Signal is in low frequency, while noise in high frequency for its weak correlation with neighboring pixel. When performing denoising, traditional spatial or frequency domain denoising algorithms is usually based on or similar to a low-pass filter which can filter off the high-frequency components of the signal. However, some information mutations(e.g. edge feature) are also in high frequency, and these information mutations have more impact on image visual effects. So how to filter off image noise while maintaining better image texture details becomes the hot spot in image denoising field.Image denoising technology based on PDE(Partial Differential Equation) is an adaptive denoising method. During the process of denoising, image features with their directions and magnitude are detected. Less smoothness in the locations with strong image features, more smoothness in the locations with weak image features, and maximal smoothness in the directions along the image features. This can smooth image noises away while preserving edges well. So it is a good denoising technology.This thesis is organized as follows:In the first chapter of the this thesis, the digital image processing technologies are simply introduced and the significant role played by the technologies in dealing with image is also stated. As a key step in the the digital image processing, image denoising has a great influence on the effect of image processing. In this chapter, various technologies of image denoising are discussed. The advantage of applying partial differential equations (PDE) to the digital image processing is also discussed in this chapter.In chapter 2, the commonly used noise removal methods are introduced including simple linear average, spatial low-pass filters, order statistic filters and wavelet transforms. The history and development of image denoising methods based on PDE is introduced at the end of the chapter.Intensive study is given to PDE based image denoising models in chapter 3. We derive PDE from both the view of energy variation and filtering. We made intensive study to the distribute fiinction's characteristics of P-M equation. Moreover, we studied the mechanism of PDE based noise removal in local coordinates.In chapter 4,I derived two improved methods of anisotropic diffusion based on the former chapter's analysis. The first is that PDE still can not preserve fine image structures like corners well enough. We can judge image egde better by using a curvature mode operator rather than gradient operator. The second is that we made a research of the gradients in the same template and get a more precise measure of image edge judging.Using the methods, less misjudge of image edge will be made. The models of these two methods are given and the numerical solution of the models are discussed, too.We made simulation experiments in the last chapter. By this, we verified the validation of our models. It shows that both methods are good edge-preserving with efficient denoising effect.But what's needed to say is that the noise used in experiments is ideal, and it is always regarded as additive Gaussian noise or pulse noise. In fact, noise is more complex. So many denoising methods should be used when we want ideal performance.