Wavelet Thresholding Via Non-Gaussian Distribution And Context Modeling

I have engaged in image denoising research for a half and one years, during which I also participated in the development of segmentation of magnetic resonance brain images project, and meanwhile, I also made some corresponding research work, aiming at image denoising. A new spatial adaptive wavelet thresholding method is presented, which is based on a non-Gaussian bivariate distribution and context modeling for image denoising that is inspired by image coding. This denoising algorithm is also applied in the image preprocessing for magnetic resonance imaging project and have achieved excellent result. This thesis has started within the context of a project on magnetic resonance imaging, in which image denoising is one of the fundamental preprocessing steps. A MRI image might be degraded by white noise leading to a significant reduction of its quality. Some of the noise originates in the acquisition hardware, others are of physiological origin. In order to achieve a good performance in segmentation of magnetic resonance brain images, a more precise and efficient image denoising algorithm is needed. In general, image denoising imposes a compromise between noise reduction and preserving significant image details. So in order to balance them well, denoising algorithm has to adapt to image discontinuities. The wavelet representation naturally facilitates the construction of such spatially adaptive algorithms. It compresses the essential information in a signal into relatively few, large coefficients, which represent image details at different resolution scales. Therefore a new spatial adaptive wavelet thresholding method is presented, which is based on a non-Gaussian bivariate distribution and context modeling for image denoising that is inspired by image coding. The dependency between coefficients and their parents is carefully studied and a new distribution model is proposed, which is composed of two variables and a free parameter. Context modeling is the core method in image coding and is applied in this project for choosing the spatial adaptive threshold that is derived in a Bayesian framework. Experiment results show that this new method outperforms the best recently published methods, such as SureShrink, Wiener2, and BayesShrink. This thesis focuses on following items: (1) introduce to wavelet in image denoising (2) review on image denoising algorithms based on Bayesian statistical models (3) present our main contributions to wavelet denoising based on non-Gaussian distribution and context modeling. We show the difference between our distribution and generalized Gaussian distribution and the advantages over it. And context modeling method is also introduced and shown how to use it to obtain the wavelet coefficients'estimate. (4) show the application of our algorithm to magnetic resonance imaging project. The thesis is organized as follows. In Chapter 1, we show the situation,, topical outline of image denoising and its current research trends. In Chapter 2, we introduce the background knowledge on wavelet theory to you. In Chapter 3, we briefly review on Bayesian statistics and image denoising algorithms based on Bayesian statistical models. In Chapter 4, we present our main contributions to wavelet denoising based on non-Gaussian distribution and context modeling. Chapter 5 is devoted specifically to image denoising in magnetic resonance imaging project. Chapter 6 gives the summary of the whole thesis.