Fast computation of the compressive hyperspectral imaging by using alternating least squares methods

Hyperspectral imaging acquires up to several hundreds of narrow and adjacent spectral band images simultaneously. However, since the dimension of the hyperspectral imaging data, which typically forms a third order tensor, is increased in proportion to the size of spatial and the spectral information at the same time, the higher order singular value decomposition (HOSVD) is appropriate to reduce its dimension. One of the simplest and most accurate approaches for computing the HOSVD is higher order orthogonal iteration (HOOI), which computes the factor matrices from the unfolding matrices of the given tensor by using singular value decomposition alternatively until convergence is achieved. However, because of its expensive computational complexity, we propose a faster algorithm to compute the HOSVD even though the output shows no meaningful difference from that obtained by HOOI. Specifically instead of computing the factor matrix from the updated tensor in every iteration along each mode, we reuse the intermediate result after updating one factor matrix to modify the others in a single iteration. Numerical experiments reveal that the proposed algorithm computes the dimension-reduced hyperspectral imaging much faster than HOOI with fewer outer iterations. Moreover, the difference in accuracy between the proposed algorithm and HOOI is negligible.