Journal of Algorithms
Rank, decomposition, and uniqueness for 3-way and n-way arrays
Multiway data analysis
Matrix computations (3rd ed.)
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
Generalized Hilbert scan in image printing
Proceedings of the 6th Workshop on Theoretical Foundations of Computer Vision
Facial Expression Decomposition
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Multidimensional filtering based on a tensor approach
Signal Processing
DOA estimation in multipath: an approach using fourth-ordercumulants
IEEE Transactions on Signal Processing
Applications of cumulants to array processing. III. Blindbeamforming for coherent signals
IEEE Transactions on Signal Processing
Blind PARAFAC receivers for DS-CDMA systems
IEEE Transactions on Signal Processing
Parallel factor analysis in sensor array processing
IEEE Transactions on Signal Processing
Detection of the foveal avascular zone on retinal angiograms using Markov random fields
Digital Signal Processing
ACIVS'07 Proceedings of the 9th international conference on Advanced concepts for intelligent vision systems
Multidimensional noise removal method based on best flattening directions
ACIVS'07 Proceedings of the 9th international conference on Advanced concepts for intelligent vision systems
A survey of multilinear subspace learning for tensor data
Pattern Recognition
Multiway filtering applied on hyperspectral images
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
Edge-preserving color image denoising through tensor voting
Computer Vision and Image Understanding
A New Truncation Strategy for the Higher-Order Singular Value Decomposition
SIAM Journal on Scientific Computing
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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-(K"1,...,K"N) 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.