The main research issue of this dissertation is to find the low-rankness of implicit low-rank data. It contains noise modeling, feature space learning, and data expression for High-dimension Image/Feature Recovery via low-rank methods. The main research contents of this dissertation are as follows: (1) To handle the problem of that a single image does not have explicit low-rankness in both spatial dimension and channel dimension, and the L1 norm based low-rank decomposition is difficult to be optimized due to its non-convexity and non-smoothness. We proposed the cyclic weighted median and nonlocal low-rank clustering based CWM-NLR method. First, we introduce clustering feature space to find low-dimensional subspace in the in-class image patch group with explicit low-rankness. Second, the cyclic weighted median (CWM) method is introduced to find the optimal solution by solving a series of scalar minimized convex subproblems. The proposed method not only solves the problem of weak explicit low-rankness of the single image, but also has good convergence and low computational complexity. (2) Most of the existing feature spaces for converting implicit low-rank data to explicit low-rank data are artificially designed and rely heavily on human experience and specific fields. To solve this problem, a general data-driven feature space is proposed in this dissertation. It has a stronger low-rankness than the original observation space, so the performance of the existing low-rank models can be improved in the feature space. In addition, feature maps also show sparsity, hence we propose the feature sparse measure Sfea, and the Sfea based nonlocal low-rank denoising model (Sfea-NLR). Extensive experiments validate the superiority of our work. (3) This dissertation propose a denoising model based on LP norm and enhanced three-dimensional total variational regularization (E-3DTV) for the restoration of hyperspectral images. First, 3DTV regularization assumes that the gradient feature space of hyperspectral has sparse structure with independent identical distribution. However, gradient maps usually have different and correlated sparse structures in all bands. E-3DTV effectively encodes the correlation and difference of sparse structures by imposing sparse constraints on the low-dimensional subspace of gradient maps. Second, L1 norm is usually used in hyperspectral image restoration task, which makes the model only effective against Laplace noise. In order to improve the adaptability to real scenarios, we proposed a Lp norm based E-3DTV denoising model. Extensive experiments validate the robustness of our method under different noise conditions. (4) The traditional robust principal component analysis (RPCA) model uses matrix to express high-dimensional tensor data, which destroys the inherent structural information. In addition, it is difficult to deal with the unknown and complex real noise via L1 norm. Therefore, this dissertation proposed a tensor RPCA model called TenRPCA-MoG based on Mix of Gaussian (MoG) and CP decomposition. Using tensor structure to express raw tensor data allows us to make full use of the inherent structure priors of data. MoG is a general approximator to any blends of consecutive distributions, which makes our method capable of regaining the low dimensional linear subspace from a wide range of noises or their mixture. The model is solved by a new proposed algorithm under a variational Bayesian inferred framework. The superiority of our approach over the existing state-of-the-art approaches is validated by extensive experiments on both of synthetic and real data.