Image Inpainting Based On Tensor Decomposition And Weighted Nuclear Norm

With the progress of society and the development of science and technology,people will generate a large amount of image data every day.The image will be af-fected and degraded by various factors during the transmission and storage process.This has promoted the vigorous development of digital image processing technol-ogy.Digital image inpainting technology is an important part of image processing.Its main purpose is to complete the image that has lost part of the pixels,making it to be the original state.Digital image inpainting technology has been used in historical research,astronomical research,medicine research and other fields.In fact,for a damaged image,the location of the missing pixels can be roughly divided into two categories,namely,random loss and special loss.And the loss of the entire row or column of the image is a very hard problem to deal with.At present,the matrix low-rank inpainting algorithm can not handle this special structural loss well.The diffusion-based method is easy to produce blur,the exemplar-based method is prone to error filling,and the neural deep learning-based method is highly dependent on training data.In this paper,the patch-based non-local self-similarity is used to process the image,and the tensor completion algorithm based on low rank prior is applied to the similar tensor completion.Also the weighted nuclear norm is added to the tensor completion model to further improve the algorithm.The main work of this article includes:1)An image inpainting algorithm based on similar tensor completion is pro-posed.First,the image is divided into patches,called reference pathces,and for each reference patch we search similar patches by a certain distance metric.The difference betweent traditional methods and ours is that we directly stack these patches into a three-dimensional similar tensor instead of pulling it into column vectors and forming a similar matrix.Then the similar tensor is completed by the tensor completion algorithm.At last,we aggregate all of the estimated patches to produce the final inpainted image.Experiments prove that this algorithm can effectively restore the image with column loss and keep the details,compared with the matrix low-rank algorithm.2)An image restoration algorithm based on weighted strategy-based tensor com-pletion is proposed.Since the weighted nuclear norm is a better approximation to the rank function than nuclear norm,we replace the nuclear norm in the original tensor completion model with weighted nuclear norm.On this basis,each kernel tensor in the original model is accompanied by a weight,and the solution of the new model is given.Experimental results show that the algorithm can retain the detailed information of the image as well as better inpaint column loss.Compared with other algorithms,it has advantages in quantitative assessment and visual level.Inpainting algorithms based on low-rank priors use the similarity of image patches and perform a low-rank constraint on the similarity matrix to achieve com-pletion,but due to the specificity of column loss,the damaged image relatively has a low rank.Therefore,the matrix low-rank algorithm often fails or cannot obtain good results when dealing with such problems.The research in this paper is based on the tensor completion method,which improves the low-rank algorithms' ability to deal with column loss,and enriches the research of image inpainting.Also it can be further extended to the fields of super-resolution reconstruction and other image processing fields.