ZNIYED , Yassine

The canonical polyadic decomposition (CPD) is one of the most popular tensor-based analysis tools due to its usefulness in numerous fields of application. The Q-order CPD is parametrized by Q matrices also called factors which have to be recovered. The factors estimation is usually carried out by means of the alternating least squares (ALS)...

MIMO technology has been subject of increasing interest in both academia and industry for future wireless standards. However, its performance benefits strongly depend on the accuracy of the channel at the base station. In a recent work, a fourth-order channel tensor model was proposed for MIMO systems. In this paper, we extend this model by...

In this paper, we consider a new one-way two-hop amplify-and-forward (AF) relaying scheme with a tensor space-time coding under frequency-selective fading channels. The signals received at the destination of the multi-input multi-output (MIMO) system define a 6-order tensor which satisfies a tensor-train decomposition (TTD). We propose a new...

In the context of big data, high-order tensor decompositions have to face a new challenge in terms of storage and computational costs. The tensor train (TT) decomposition provides a very useful graph-based model reduction, whose storage cost grows linearly with the tensor order D. The computation of the TT-core tensors and TT-ranks can be done...

Multidimensional Harmonic Retrieval (MHR) is at the heart of important signal-based applications. The exploitation of the large number of available measurement diversities for data fusion increases inexorably the tensor order/dimensionality. The need to mitigate the "curse of dimensionality" in this case is crucial. To efficiently cope with...

In this work, equivalence relations between a Tensor Train (TT) decomposition and the Canonical Polyadic Decomposition (CPD)/Tucker Decomposition (TD) are investigated. It is shown that a Q-order tensor following a CPD/TD with Q > 3 can be written using the graph-based formalism as a train of Q tensors of order at most 3 following the same...

Over the last two decades, tensor-based methods have received growing attention in the signal processing community. In this work, we propose a comprehensive overview of tensor-based models and methods for multisensor signal processing. We present for instance the Tucker decomposition, the Canonical Polyadic Decomposition (CPD), the Tensor-Train...

In this chapter, we present an algebraic relation between the Tucker model and the Tensor-Train decomposition with structured cores. Exploiting this link, we present a new fast algorithm to compute the dominant singular subspaces of a Q-order tensor. As opposedt o the state of the art methods (usually called HOSVD for high-order SVD), our...