Image Denoising Research Based On Total Variation Theory

This thesis mainly studies the image denoising algorithm according to total variation principle,on the basis of the existing denoising model and its algorithm, to explore a new image restoration model.Firstly, this article simply introduces the background and significance of topic, and overviews the present situation; Then we give a brief outline of the basic knowledge of digital image, for instance, image noise model and the classification, evaluation standard of image quality, etc. And the traditional denoising methods which based on space domain and frequency domain are also presented.Total variation model is one of the most active and challenging research subjects behind digital image processing technology. For example, the classical ROF model,P-M model, etc. Due to the ROF model produces false edges- "stair casing" when the noise is removed. To make up this shortfall, many researchers put forward a number of improved models which were mainly modified in two aspects: the model itself and the numerical algorithm. On the one hand, the common models are adaptive regularization parameter, weighted variation, coupling gradient fidelity term and high order TV model, etc.; On the other hand, the numerical algorithm mainly use the optimized algorithm instead of the traditional partial differential equations method,such as gradient descent method, the original-dual method algorithm,Augmented-Lagr-ange method, ADMM and split Bregman iteration algorithm. A detailed analysis and summary is made in this paper.In the end, a novel fractional order total variation(TV) denoising scheme with a Shearlet regularization term is proposed. This model combined with the advantages and disadvantages of TV, fractional order and Shearlet transform. Besides, by applying alternating direction method of multiplier(ADMM) to solve this model, a plenty variety of experiments involving both denoising and texture extraction applications are employed to illustrate the validity of this model. Compared with other models, it highlights its advantages, and the algorithm is fast and stable.