Tensor methods for multisensor signal processing

Abstract

Over the last two decades, tensor‐based methods have received growing attention in the signal processing community. In this work, the authors proposed a comprehensive overview of tensor‐based models and methods for multisensor signal processing. They presented for instance the Tucker decomposition, the canonical polyadic decomposition, the tensor‐train decomposition (TTD), the structured TTD, including nested Tucker train, as well as the associated optimisation strategies. More precisely, they gave synthetic descriptions of state‐of‐the‐art estimators as the alternating least square (ALS) algorithm, the high‐order singular value decomposition (HOSVD), and of more advanced algorithms as the rectified ALS, the TT‐SVD/TT‐HSVD and the Joint dImensionally Reduction and Factor retrieval Estimator scheme. They illustrated the efficiency of the introduced methodological and algorithmic concepts in the context of three important and timely signal processing‐based applications: the direction‐of‐arrival estimation based on sensor arrays, multidimensional harmonic retrieval and multiple‐input–multiple‐output wireless communication systems.

Tensor local linear embedding with global subspace projection optimisation

“…And it can explore the global feature of tensor. In order to retain the local and global information of tensor, the novel TDR method is proposed by the ensemble of tensor local feature preservation (17) and global subspace projection optimisation [Equation (19)].…”

“…Tensor data represents multi-dimensional data, in which each dimension involves the inherent structure information of the original data. The TDR methods learn the low-dimensional representation of tensor data with various strategies [12][13][14][15][16][17][18][19].…”

“…Tensor decomposition is an important work for tensor-based methods, such as canonical polyadic (CP) decomposition [21], Tucker decomposition [15,22,23], tensor-train (TT) decomposition [24] and so on. CP decomposition decompresses an N-order tensor into the sum of N rank-one tensors, and is widely used in multi-sensor signal processing [17,19]. Tucker decomposition represents an N-order tensor as the mode product of a core tensor and a number of matrices.…”

Tensor dimensionality reduction via mode product and HSIC

“…Tensor analysis has been widely used in machine learning [8,17,44]. Tensor analysis (TA) [44] and tensor decomposition [45,46] are two important work for TDR.…”

“…Particularly, the matrix or 2-D data can be regarded as a special data of tensor [5,6] (the 2-D methods only suitable for 2-D images). Tensor-based methods have well performance in many application fields, such as image analysis [5,7,8], recommendation system [9,10], wireless spectrogram generation [11], seismic signals processing [12], computer vision [13], Hyperspectral image analysis [14][15][16], sensor signal processing [17] and so on. Recently, many tensor-based dimensionality reduction (TDR) algorithms have been proposed.…”