Recent advances on tensor models and their relevance for multidimensional data processing

This paper reviews the last advances which concerned tensor methods based on three main decompositions: Tucker, Parafac, and Paratuck. We show how they improved the processing of multidimensional data such as hyperspectral images and multiple input multiple output signals. First, we show how multiway Wiener filtering, based on Tucker decomposition, was set in a wavelet framework. Secondly, we remind how signal dependent noise is handled while applying the truncation of the Parafac decomposition. Thirdly, we review the sequential Parafac Paratuck decomposition and exemplify its interest for a fast characterization of channel and symbols in a MIMO framework.