A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
SIAM Journal on Matrix Analysis and Applications
Orthogonal Tensor Decompositions
SIAM Journal on Matrix Analysis and Applications
Survey on tensor signal algebraic filtering
Signal Processing
Multidimensional Noise Removal Based on Fourth Order Cumulants
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Multidimensional Noise Removal Method Based on PARAFAC Decomposition
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Fast subspace-based tensor data filtering
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Multiway filtering applied on hyperspectral images
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
On the computational benefit of tensor separation for high-dimensional discrete convolutions
Multidimensional Systems and Signal Processing
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A new multidimensional modelling of data has recently been suggested, which can be applied in a wide range of signal processing fields. Many studies have proposed new tensorial mathematical tools in order to process multidimensional data. With a view of perfecting this multidimensional model, this paper presents a new tensor approach for multidimensional data filtering. A theoretical expression of n-mode filters is established based on a specific modelling of the desired information. The optimization criterion used in this tensorial filtering is the minimization of the mean square error between the estimated signal and the desired signal. This minimization leads to some estimated n-mode filters which can be considered as an extension of the well-known Wiener filter in a particular mode. An alternating least square algorithm is proposed to determine each n-mode Wiener filter. This new multimode Wiener filtering method is tested for noise reduction in multicomponent seismic data. A comparative study with classical bidimensional filtering methods based on principal component analysis is also proposed and presents encouraging results.