Survey on tensor signal algebraic filtering

This paper presents a survey on new filtering methods for data tensor based on a subspace approach. In this approach, the multicomponent data are modelled by tensors, i.e. multiway arrays, and the presented tensor filtering methods rely on multilinear algebra. A method, developed by Lebihan et al., consists of an extension of the classical matrix filtering method. It is based on the lower rank-(K1,…,KN)(K1,…,KN) truncation of the HOSVD which performs a multimode principal component analysis (PCA) and is implicitly developed for a white Gaussian noise model. Two new tensor filtering methods developed by the authors are also reviewed. The first consists of an improvement of the multimode PCA-based tensor filtering in the case of an additive correlated Gaussian noise model. This improvement is especially done thanks to the fourth-order cumulant slice matrix. The second method consists an extension of the Wiener filtering for data tensor. The performances and comparative results between all these tensor filtering methods are presented in the case of noise reduction in color images and multicomponent seismic data.