Estimation of n-mode ranks of hyperspectral images for tensor denoising

This paper deals with n-mode subspaces in tensor based denoising. Actually, the main issue of tensor signal processing is the estimation of n-mode ranks since a subspace based approach is considered. In hyperspectral images, an efficient denoising method could allow more accurate results for classification or unmixing. In this paper, we propose to extend subspace identification methods to tensors for n-mode rank estimation. The estimation of endmembers in hyperspectral images is equivalent to estimate the 3-mode rank of a tensor. HySime and Neyman-Pearson detection theory-based thresholding method (HFC) are practical benchmarks. Therefore, we adopt tensor formalism to extend reference algorithms to determine n-mode ranks of tensors. We compare different adapted criteria both on simulated and real data.