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This paper presents a new approach for representing multidimensional data by a compact number of bases. We consider the multidimensional data as tensors instead of matrices or vectors, and propose a Tensor Rank-One Decomposition (TROD) algorithm by decomposing Nth-order data into a collection of rank-1 tensors based on multilinear algebra. By applying this algorithm to image sequence compression, we obtain much higher quality images with the same compression ratio as Principle Component Analysis (PCA). Experiments with gray-level and color video sequences are used to illustrate the validity of this approach.