Image Decomposition Based On Adaptive Direction Total Variation And G-norm Regularization

Image decomposition problem still remains an active research field in the image processing.A real image is usually the superposition of a cartoon component and a texture.Then,the cartoon component with some significant edge information is applied to evaluate the blur index,the texture component is applied to obtain the noise level,thus the significant edge structure information of the image is distinguished from the detail texture information containing noise.The cartoon component refers to the piecewiseconstant geometrical parts of an image,including homogeneous regions,contours,and sharp edges.In contrast,the texture component is about the oscillating patterns of an image,such as fine structures and local repeating features.The purpose of image decomposition is to preprocess the image according to the fact that the cartoon and texture in the image have different prior information,so as to extract the interesting information from the image.And then we can use it to carry on the subsequent computer image analysis.The primary contents of this article are as follows:· To improve the image decomposition quality,it is very important to describe the local structure of the image in the proposed model.This fact motivates us to analyze and study Meyer's decomposition model,we propose a cartoon and texture decomposition model based on the adaptive direction total variation and G-norm regularization via coupling one weighted matrix with one rotation matrix into the total variation(TV)norm.In the proposed model,the weighted matrix can be used to enhance the diffusion along with the tangent direction of the edge and the ration matrix is used to make the difference operator couple with the coordinate system of the normal direction and the tangent direction efficiently.With these operations,our proposed model owns the advantage of the local adaption and also describes the image structure more robust.· This model is applied to the noiseless synthetic images and real images.In addition,since the proposed model has the splitting structure,so the alternating direction multiplier method is used to solve it.In addition,the paper also provides theoretical analysis to ensure the convergence of the algorithm.· The comparison between the model in this paper and the existing decomposition model shows that that the proposed model and method are more robust for image decomposition problem and can achieve better performances.