Image Inpainting Using Non-Convex And Low-Rank Constraint

With the development of multimedia technology and the popularization of image acquisition equipment,images have become one of the important carriers for human beings to transmit information.However,in the process of image acquisition,transmission and storage,due to improper acquisition or transmission and other factors,the obtained image may be damaged,which brings inconvenience to the follow-up work.Therefore,it is necessary to recover the missing information in the image and improve the visual effect of the damaged image.Due to the different shapes of the missing regions of the image,different types of corresponding inpainting methods have been proposed.Based on the study of these methods,this paper focuses on the image inpainting method based on low-rank representation.This kind of methods use the nuclear norm to model the low-rankness of the image.However,the nuclear norm imposes equal penalty on different singular values,which leads to the details information of the image cannot be well preserved.To solve the above problems,this paper made the following improvements :1.We propose an image inpainting method based on nonconvex low rank matrix completion.Image inpainting based on low rank matrix completion is generally modeled by a rank function.Because the rank function of a matrix is nonconvex and discrete,solving the model is a NP-hard problem.So the matrix nuclear norm is widely used to relax the rank function.However,in real data recovery,this convex relaxation solution may deviate from the solution of the original problem.Studies have shown that some nonconvex functions can approximate the rank function better than the nuclear norm.Therefore,we use the log function to approximate the rank function in the low-rank matrix completion model.In addition,due to the non-convexity of the objective function,this model is difficult to solve directly.Therefore,we use Taylor expansion to approximate the log function linearly,and use alternating direction multiplier method to solve this new model.The experimental results show that the proposed algorithm is effective in inpainting images and maintaining the details information of images.In other words,our method has certain advantages in both visual effects and quantitative indicators.2.We further propose an image inpainting method based on non-convex low-rank tensor completion.In the applications,the color images need to be inpainting are three-dimensional,which can be represented by tensor.Although the inpainting algorithm based on matrix completion has been mature,the method of expanding tensor into matrix for image inpainting destroys the structure of the image itself,so we propose an image inpainting algorithm based on low-rank tensor completion.The difficulty of this algorithm is that the definition of rank is not unique,including CP-rank,Tucker-rank and tube rank defined based on tensor singular value decomposition(t-SVD).Combining the advantages of t-SVD and Tucker-rank decomposition,this paper proposes an image inpainting algorithm based on low-rank tensor completion.From the above low rank matrix completion algorithm,it can be known that the solution obtained by convex relaxation of rank function using nuclear norm may deviate from the solution of the original problem,in order to reduce this deviation,we still use the log function to approximate the rank function in the low-rank tensor completion model.In order to solve the problem efficiently,the original problem is decomposed into multiple sub-problems by using the alternating direction multiplier method.The experimental results show that the algorithm has good performance.In general,based on the inherent low-rankness of the image itself,this paper studies modeling through log functions.By constructing the non-convex low-rank matrix completion algorithm and the non-convex low-rank tensor completion algorithm,the key problem of equal penalty of different singular values by nuclear norm is solved.The experimental results show that the proposed algorithm can obtain better results than most existing image inpainting algorithms.