Hyperspectral imaging is widely used to many applications as it includes both spatial and spectral distributions of a target scene. However, a compression, or a low multilinear rank approximation of hyperspectral imaging data, is required owing to the difficult manipulation of the massive amount of data. In this paper, we propose an efficient algorithm for higher order singular value decomposition that enables the decomposition of a tensor into a compressed tensor multiplied by orthogonal factor matrices. Specifically, we sequentially compute low rank factor matrices from the Tucker-1 model optimization problems via an alternating least squares approach. Experiments with real world hyperspectral imaging revealed that the proposed algorithm could compute the compressed tensor with a higher computational speed, but with no significant difference in accuracy of compression compared to the other tensor decomposition-based compression algorithms.
The Epsilon-Alternating Least Squares for Orthogonal Low-Rank Tensor Approximation and Its Global Convergence