The Generalized Higher Order Singular Value Decomposition and the Oriented Signal-to-signal Ratios of Pairs of Signal Tensors and their Use in Signal Processing

Abstract:  Abstr act - Two new generalizations of tenso r concepts for signa l processing are presented. These generalizatio ns are typically relev ant for appli cations where one tenso r consi sts of valua ble measured data or signa ls, that shoul d be retai ned, while the second tenso r conta ins data or information that shoul d be rejected. First the higher order singular value decomposition for a singl e tenso r is extended to pairs of tenso rs; this is the multi linear equiv alent of the generalized or quoti ent SVD (GSVD, QSVD) for pairs of matri ces. Next the notio n of oriented signa l-tosigna l ratio s that was deriv ed for pairs of matri ces is extended to pairs of tenso rs. These signa l to signa l ratio s can be linked to the previ ously defined generalized higher order singular value decomposition. 1