Low-rank filter and detector for multidimensional data based on an alternative unfolding HOSVD: application to polarimetric STAP

This paper proposes an extension of the higher order singular value decomposition (HOSVD), namely the alternative unfolding HOSVD (AU-HOSVD), in order to exploit the correlated information in multidimensional data. We show that the properties of the AU-HOSVD are proven to be the same as those for HOSVD: the orthogonality and the low-rank (LR) decomposition. We next derive LR filters and LR detectors based on AU-HOSVD for multidimensional data composed of one LR structure contribution. Finally, we apply our new LR filters and LR detectors in polarimetric space-time adaptive processing (STAP). In STAP, it is well known that the response of the background is correlated in time and space and has a LR structure in space-time. Therefore, our approach based on AU-HOSVD seems to be appropriate when a dimension (like polarimetry in this paper) is added. Simulations based on signal-to-interferenceplus-noise ratio (SINR) losses, probability of detection (Pd), and probability of false alarm (Pfa) show the interest of our approach: LR filters and LR detectors which can be obtained only from AU-HOSVD outperform the vectorial approach and those obtained from a single HOSVD.