The Research On Filtering Methods Based On Improved Variational Image Decomposition Algorithms And Their Application

Image filtering has always been the significant step among image processing,which bring important influence to further image analysis.Variational image decomposition algorithm has a broad development prospect,it belongs to the categories of variational method and the study of the partial differential equation of image processing.Its main steps can be briefed as follows: firstly it decomposes an image into two or more parts that are described by corresponding and appropriate function spaces,then constructs the energy functions by combining norms of different spaces and lastly works out the results by minimizing the energy functions.In this text,we have proposed novel decomposition algorithms based on published methods,and we have put these new methods into use to filter Gaussian noise and speckle noise.We will explain the excellent filtering performance of these new methods by giving numerical simulation analysis and comparison of visual effect.The main contributions of this text can be summarized as follows:1.Based on the block matching 3-D algorithm(BM3D),we have proposed an image decomposition model named TV-G-BM3 D for filtering Gaussian noise.The performance of decomposition algorithm has been great improved by putting BM3 D into use to model noise.We test the proposed method on the four images corrupted by Gaussian noise with different degrees and compare it with the four other image decomposition methods.The comparisons of visual effect and the three assessment indices confirm that the excellent denoising performance of proposed models.2.Based on nonlocal data fidelity term,we have optimized previous variational image decomposition algorithms for filtering Gaussian noise.The development from referencing adjacent pixel value in the image to referencing every pixel value,the nonlocal framework will bring benefits to the image decomposition methods.We combine the nonlocal data fidelity term with the2TV-Hilbert-L model and TV-G-Shearlet model.We test their performance by putting them into use to filter standard figures contaminated by different level Gaussian noise and compare the proposed method with primary image decomposition methods by means of giving quantitative comparison and showing the visual effects,which confirm that excellent denoising performance of improved models.3.Based on the framework of total generalized variation,we have proposed new fringe patterns denoising model2TGV-Hilbert-L for filtering speckle noise.Compare to lower order derivatives of a function,higher order derivatives of a function will bring more smooth result which will avoid staircase effect.We test proposed model by putting it into use to process simulative fringe figure and electronic speckle shearogarophy pattern interferometry deficient detection patterns compare it with published fringe figure processing methods.It can be found that our proposed model perform best by referencing quantitative comparison and visual effects.The achievements of this paper enrich the theory of variational image decomposition.