Three-mode data set analysis using higher order subspace method: application to sonar and seismo-acoustic signal processing

• Authors: Nicolas Le Bihan;Guillaume Ginolhac
• Venue: Signal Processing
• Year: 2004

In this paper, a three-mode subspace technique based on higher order singular value decomposition (HOSVD) is presented. This technique is then used in the context of wave separation. It can be regarded as the extension to three-mode arrays of the well-known subspace technique proposed by Eckart and Young (Psychometrica 1 (1936) 211) for matrices. Three-mode data sets are increasingly encountered in signal processing and are classically processed using matrix algebra techniques. The proposed approach aims to process naturally three-mode data with multilinear algebra tools. So in the proposed algorithms, the structure of the data set is preserved and no reorganization is performed on it. The choice of HOSVD for subspace method is explained, studying the rank definition for three-mode arrays and orthogonality between subspaces. A projector formulation for three-mode signal and noise subspaces is also given and the improvement of separation with the three-mode approach over a componentwise approach is shown. We study two applications for the proposed Higher Order Subspace approach: the reverberation problem in sonar, and the polarized seismo-acoustic wave separation problem. For the first application, we propose a three-mode version of the Principal Component Inverse algorithm (IEEE Trans. Aerospace Electron. Systems 30(1) (1994) 55). We apply the proposed technique on simulated data as well as on real sonar data where the three modes are angle, delay and distance. For the second application, we consider the polarization of the seismic wave as the third mode (in addition to time and distance modes) and show the resulting improvement of wave separation using the proposed Higher Order approach.