Research On Image Completion Algorithm Based On Tensor Singular Value Decomposition

With the rapid development of digital technology,digital images have become an essential media form.However,during the process of acquisition and transmission,image data may suffer from missing data due to factors such as noise,camera shake,and resolution limitations,which can lead to inaccurate,unreliable,and unpredictable results in subsequent computations.Therefore,how to recover complete images from incomplete observation data has become an important research area.Typically,image/video information presents a high-dimensional structure that can be viewed as a low-rank or approximately low-rank structure.As a result,researchers have conducted studies on low-rank tensor completion based on the low-rank prior of tensors.Low-rank tensor completion can be viewed as an application of tensor decomposition,which decomposes the original high-dimensional data tensor into the product of multiple low-rank tensor factors and utilizes partial information of known data to determine these low-rank tensor factors.Among them,the low-rank tensor completion method based on tensor singular value decomposition(t-SVD)has been widely used in many fields.This thesis is based on t-SVD and combines with the prior knowledge of images to study image completion based on tensor rank minimization constraints.1.This thesis proposes a low-rank tensor completion model based on non-local selfsimilarity,aiming to enhance the low-rankness of the image to better explore the inherent low-rank structure of tensor data.Specifically,for the problem of color image restoration,the general processing method is to regard it as a three-dimensional tensor and approximate it with tensor nuclear norm.However,although this tensor has certain low-rankness,it does not have strong low-rankness.To enhance the low-rankness of the image,this thesis utilizes the non-local self-similarity characteristics of the image and enhances the low-rankness of the tensor by extracting non-local self-similarity tensor blocks.On each tensor block,this thesis uses tensor nuclear norm minimization for completion and uses the alternating direction multiplier method for optimization.Furthermore,an adaptive mixed threshold operator is proposed for the optimization solving process,which can adaptively estimate the number of truncated singular values and use a combination of soft and hard thresholding to perform singular value shrinkage.This approach can better approximate the rank of the original matrix and restore the details and texture structure of the image.The proposed method shows promising results in image denoising and inpainting tasks,indicating its potential in practical applications.Finally,the proposed algorithm is applied to the restoration of color images and grayscale videos,and experimental results show that the algorithm has significant advantages in restoring image details and texture structures.2.This thesis proposes an improved Tensor-Truncated Nuclear Norm(T-TNN)model,which employs a non-convex γ function instead of the nuclear norm used in the traditional T-TNN model as a surrogate function for rank function.The nuclear norm,which is used as a convex surrogate function for the rank function in the traditional T-TNN model,has limited approximation ability,resulting in poor algorithm performance.Therefore,this thesis adopts a non-convex γ function to replace the nuclear norm as the low-rank term in the T-TNN model and analyzes the theoretical reasons why the non-convex γ norm better approximates the rank function than the nuclear norm.The proposed algorithm is solved by the Generalized Alternating Direction Method of Multipliers(GADMM),and extensive experimental results validate the effectiveness of the proposed algorithm.