Research And Applications Of Tensor Learning And Low Rank Recovery Algorithm

With the rapid development of science and technology,portable intelligent devices,unmanned aerial vehicles,and remote sensing satellites have broadened our ability to recognize the world,but also brought us highdimensional data with more complex structures.Nonetheless,due to the interference of internal and external factors in the acquisition,transmission and storage process,the observation data may be degraded by Gaussian noise,impulse noise,salt and pepper noise,and stripe noise,which will gravely affect the subsequent applications.Accordingly,it is important and valuable to restore clean data from the observed data by noise pollution in computer vision,data mining,and machine learning.Recovering low-rank clean components and noise components from observed data is an ill-posed problem in mathematics.The low-rank recovery algorithm based on low rank and sparsity prior information is an effective way to solve this problem.However,when processing high-dimensional data,the compressed sensing theory based on vector and the matrix-based low-rank recovery algorithm will destroy its internal structure and cause unnecessary information loss.Hence,tensors have attracted a lot of attention because they can preserve the multi-linear structure of high-dimensional data.In this thesis,the low-rank recovery problem is studied based on the tensor singular value decomposition(T-SVD)framework and applied to color image and hyperspectral image denoising tasks.The main work of this thesis is as follows:(1)An enhanced robust tensor principal component analysis algorithm(E-TRPCA)is proposed.Focus on the problem of the excessive dependence of the original RPCA and its improved model on the low-rank structure of the input data and the high computational complexity,we adopt the double decomposition strategy to learn a basis tensor and coefficient tensor,which can effectively reduce the computational complexity of singular value decomposition.In addition,a new enhanced tensor kernel norm(E-TNN)regular term is constructed.To naturally reflect the intrinsic structure of the tensor and improve the generalization of the model,E-TNN restricts the lowrank property of the tensor data via its low-dimensional subspace bases.The augmented Lagrange multiplier method is used to optimize the objective function.Compared with other similar methods,experimental results on image restore and background Modeling verify the effectiveness and generalization of our method.(2)A hyperspectral image denoising model based on t-SVD and enhanced3 D total variation(E3DTV)is proposed(T-E3DTV).The model exploits the tensor tubal rank to explore the global spectral correlation of hyperspectral images and applies the E3 DTV regularization term to explore the local correlation of hyperspectral images.T-E3 DTV generalizes the E-3DTV model from matrix to tensor,which preserves the structural information of hyperspectral images and improves the denoising performance of the algorithm.An augmented Lagrange multiplier algorithm is designed to resolve the proposed model.Numerical experiments demonstrate that the proposed method can well remove sparse noise and streak noise from the data.