Research On Several Optimization Algorithms For Image Denoising

Image is the main sources of information for human beings. Digital image processing has become an important method of acquiring, processing, analyzing and sharing for human beings in an information age, and it has already penetrated with the different aspects of the human’s production and life with huge social and economic benefits. In particular, by combining cognitive psychology, machine learning and machine vision in recent years, image processing sparks new developments and breakthroughs. Therefore, the relative research of digital image processing makes a significant sense in theory and a broad prospect in practical application.Image denoising is a kind of technology in the fields of digital image processing. It is the key step in the underlying processing, thus the effect of the processing can affect the performance of the successive stages, such as segmentation, recognition and analysis. With the development of science and technology, various parts in image processing increase continuously to the request of the image quality. Thus, the research on effective denoising algorithms and the improvement of the performance of denoising are very necessary and important. It provides a solid grounding for the successive stages.This paper takes deep research on image denoising algorithms based on order statistical, variational regularization, variational inequality and noise detection algorithm based on local features. By analyzing shortcomings and deficiencies, further improved algorithms are proposed, and their effects are assessed both in theory and experimental examinations. The main work of this thesis includes the following aspects:(1) By analyzing the conflicts between noise suppression and edge preservation, an improved denoising method combined with weighted spatial outlier measurement and optimized regularized energy functional is proposed. In the first phase, the weight from image local features is affected outlier measurement, which makes the measurement be sensitive to edge detail. It enhances the identification capability of difference between edge and impulse noise. The algorithm has been optimized for two aspects in filtering phase based on noise candidate set generated in first phase. Firstly, the data-fitting term has been optimized by the separation between noisy pixels and free pixels. The optimization reduces difficulty of function minimization and improves efficiency of the algorithm. Secondly, the interference of noise is reduced by splitting function scope when noisy pixel is recovered. In the end, edge-preserving regularization has been assigned the ability of noise suppression while edge preservation by introducing local features.(2) For the problem of accuracy of impulse noise detection in complex images, this paper provides optimizing schemes in two aspects and generates enhancement detection approach for impulse noise. First, the capability of noise detection for edge has been enhanced by introducing directional property of edges. The significant difference between object pixel and its neighborhood is the common character of edge and noise. However, the stronger directivity of natural image can provide a breakthrough for distinguishing the two. The enhancement method suppresses the interference between edge pixels and noisy pixels by increasing the weight in ordered statistics which belong to the local optimized direction. It improves the detection capability on image edges, and provides a solid foundation for restoration. Meanwhile, based on the mean value from the defined sub-neighborhood, the method suppresses the interference of noisy pixels in neighborhood, and improves stability of the algorithm. Secondly, the adaptation of threshold value has been improved by introducing adaptive mechanism. After analyzing the conflicts between different patterns and fixed global threshold value, an adaptive threshold method based on local mean value and standard deviation is proposed. It improves the adaptive capacity for different image patterns areas, such as flat areas, edge structure and textures detail.(3) Variational inequality theory, an important tool for solving minimization problem, can play an important role in denoising and deblurring when the image denosing and deburring are regarded as optimization problem with discrete total variation regularzation. However, the related research results are relatively fewer. Following the framework of variational inequality,this paper introcuces a general total variation regularzation including kinds of particular total variations to propose a new denosing and deblurring method. The proposed general method includes kinds of adaptive and anisotropy total variation.(4) In order to further study the image denosing and deblurring problem based on solution-driven adaptivity general total variation regularization,this paper proves the existence and uniqueness of the solution for mixed quasi-variational inequality. On this basis, this paper introduces a modified projection algorithm for solving the mixed quasi-variational inequality and gives a proof of its convergence. It provides a theoretical basis for the development of denosing and deburring based on variational inequality.