Partial Differential Equations-based Image Denoising

"Image processing has been an active research field resulting from the development of computertechnology and increasing requirements of multimedia data processing. Since image denoising andenhancement are often applied to improve the image quality and to make them fulfill the applicationrequirements, both of them are important research subjects in image processing. In this paper, moreattention is paid to the partial differential equation based methods, especially to introduce the structureinformation to the these methods proposed in the literature. We have reviewed and studied thefollowing topics: the axiomal PDEs based on scale space theory, variational PDEs and geometricalPDEs based on curve or surface evolution in this thesis. The difficulties of them are analyzed andsolutions to them are proposed.Some novel models and algorithms have been proposed as following:1) A number of image processing and computer vision tasks make use of linear structure tensor.Unfortunately, linear filter method is well-known to destroy the important structures. So we can notget well results by linear structure tensor. In this paper, we propose a improved method, whichemploys the canny operator and linear structure tensor to get a better structure estimation results.2) Investigates the performance of Total Variation Flow for noise removal and preservingstep-edge from the view of level set curve. In order to improve the performance, structure informationis introduced and a new method that uses structure information and Total Variation is constructed. Theremoval is done in two steps. We first use improved linear structure tensor to get the structureinformation of the noise image. After this, we try to use the information and the Total Variation flowto remove noise. When used for grayscale image noise removal, this new approach circumvents theTotal Variation flow. Compared to the Total Variation model, the method is effective on the noiseremoval of slope images and cannot cause staircase effect.3) Proposes a new adaptive fidelity term, which is obtained from image local structuralinformation. At first, we discuss three requirements of noise removal method. After this, we propose anew coupling adaptive fidelity term for the tensor-driven diffusion filter. Experimental results showthat the approach with our new fidelity term is capable of sufficiently preserving geometricinformation, such as edges and comers,in addition to its effectiveness for noise removal.4)Propose a texture preserving fourth order partial differential equations basedIamge denoising model which preserves texture well. At first, a cost functional relying on secondderivatives of image intensity function in succession. The method is tested on a borad range of realimages and demonstrates good noise suppression without destruction of important edges and textures in the image.