1. A method for recovering a low-rank matrix A, noise, and a subspace from data in a form of a high-dimensional matrix X, comprising the steps: representing an objective function as min E , D , α  α  row - 1 + λ  E  1 , such that 
 Dα+E=X,D T D=I k ; minimizing the objective function to solve for E, D, and α, wherein the high-dimensional matrix is Xε m×n , the low-rank matrix with rank r=min{m,n} is A=Dα, the subspace D is spanned by D=[D 1 , D 2. .. , D k ]ε m×k , α are coefficients α=[α 1 ; α 2 ;. .. ; α k ] ε k×N , α i specifies a contribution of D i to each column of the low-rank matrix A, E is a sparse matrix representing the noise in the data, ∥α∥ row−1 =Σ i=1 k ∥α i ∥ 2 is a sparsity inducing row−1 norm, ∥E∥ 1 =Σ i=1 m Σ j=1 n |E ij | is an l 1 norm, T is the transpose operator, I k is an k×k identity matrix, and λ is a weighting coefficient; and assigning the low-rank matrix as A=Dα and the noise matrix as E, wherein the steps are performed in a processor.