Research Of Image Denoising Problem Based On The Two-dimensition Low-rank Regularization

In the process of image formation, transmission and storage, inevitably willintroduce some noise, thus seriously affect the quality of the image, and bring greatdifficulties for analysis and other follow-up work, so image de-noising is an importantresearch in the filed of image processing. The purpose of de-noising is to eliminate thenoise in the image as far as possible while preserving the information of originalimage.In recent years, regularization method attracted extensive attentions and wassuccessfully applied to technology of image restoration, image restoration and otherclassical inverse problems. The inverse problem is usually an ill-pose problem, andregularization method is an effective approach to solve such problems. The imagede-noising is one of the important work of image restoration. From the beginning ofthe1990s, the Total Variation (TV) regularization method of image de-noisingtechnology has been proposed. The total variation of images which contains noise willbe bigger than clean images, so the total variation minimization can eliminate thenoise in the image, which is modeled as an energy function minimization problem inthe image de-noising problem. Total variation is an edge-preserving filter because inthe process of de-noising, the anisotropic diffusion equation is introduced, the edgeand other detail features will be kept well while the smoothing process. In recent years,the sparse theory successfully applied to the image de-noising problem due to itspracticality and convenience. Sparse theory is based on the premise that under someconditions one image can be linearly represented by the combination of an overcomplete dictionary, and the representation coefficients should be sparse. For animage contaminated with noise, one can choose or design an appropriate dictionaries,and got the sparse representation of noisy image under given dictionary, to achieve thegoal of de-noising.This thesis aim at the de-noising of image contaminated by poisson noise. Ourmodel is under the frame of maximum a posteriori probability, and usingtwo-dimensional low rank as the regularization. The likelihood function from theMAP will be used as the data fidelity term in the model, and the low rank as the regularization of the image structure, finally in order to keep the image is not negative,we introduce a nonnegative constraint.Another work of this thesis is a smooth approximation of low rank regularizationis proposed, which put forward a new direct regularization method to solve theoptimization problem of low rank. Contrast to nuclear norm approximation, wepropose a smooth approximation of rank regularization by adopting the gaussianfunction as the approximation function. Its advantage is that it can directly solveproblem of rank regularization problem, and in the process of calculation only need tocalculate singular value decomposition once, which improve the computationalefficiency. In view of the regularization parameter selection problem, this paperstudies the automatic selection method based on Morozov deviation principle.