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

*Correspondence: [email protected] 1SATIE, ENS Cachan, 61, av President Wilson, 94230 Cachan, France Full list of author information is available at the end of the article Abstract 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 Interference plus 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.