Research On Image Completion Algorithm Based On Low-rank Tensor Decomposition

Visual data such as images is an important source of information in people’s daily lives,and a variety of internet applications and related scientific research equipment have generated massive amounts of data.However,in the process of collecting and converting original image’s data,due to sensor’s failure or the degradation of environment,some elements may lossed and cause the collection incomplete then result in reduced image quality.Subsequent analysis of the image and relevant applications may also be difficult to guarantee.The use of known elements to complete missing parts through low rank tensor decomposition has received a lot of attention.In recent years,tensor ring decomposition has become more flexible and efficient in representing high-order data,and has also been widely applied in data completion.This article is based on tensor ring decomposition and explores other potential prior information of images while constructing low rank hypotheses.In addition,the rank selection of tensor ring decomposition has always been a challenge.This article constructs a Bayesian model for adaptive rank determination.The main research is as follows:1.Research on tensor ring completion algorithm based on low rank prior and nonlocal self-similarity prior.By using the tensor ring neclear norm as the low rank constraint structure in the model and explore the non-local self-similarity information in the image simultaneous.We explore the completion of missing data in image on two kinds of prior knowledge.The proposed algorithm describes the low rank structure by tensor ring nuclear norm,and realizes the weighting of different singular values by logarithmic determinant function working on the nuclear norm.Unlike manually designed non-local regularization operators,this article introduces the BM3 D denoising operator through the Plug and Play framework(Pn P)as a regularization in the model to explore the non local similarity of images as supplementary information for completion.The proposed algorithm combines the low rank assumption and potential knowledge of non-local in image.On the one hand,it approximates the characterization of low rank by the weighted nuclear norm,and on the other hand,it improves the completion performance by utilizing the distant non-local information of image.The experimental results of the proposed algorithm were presented on multiple datasets and compared and analyzed with other methods.2.Research on the completion algorithm based on tensor ring rank adaptation.The low rank representation of tensor rings can be well used for completing missing data,but the tensor ring rank needs to be manually fixed in advance.Since the rank of tensor ring is given in vector form and the scale space increases with the increase of tensor dimension,it has always been a difficult problem to determine a good rank of tensor ring.The proposed algorithm constructs a complete Bayesian probability model for the derivation of tensor ring rank,thereby adaptively determining the selection of tensor ring rank.For real image data,the low rank assumption can meet certain characterizations.However,in reality,many image data only approximate low rank structures,and there are also some details in the image that can be called non low rank structures.The proposed algorithm utilizes Gaussian mixture distribution in the Bayesian framework to fit the detailed information in the image to further improve the performance of completion.The effectiveness of the proposed algorithm was verified through experiments.