Signal Processing based on Multilinear Algebra

By Lieven De Lathauwer. 1997

Subfields: Numerical Methods & Scientific Computing, Signal Processing

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Another consequence of the relation (4) is the higher-order SVD (HOSVD) introduced in [55, 56] for approximating a tensor by a Tucker decomposition (3) of lower multilinear rank.”
Image Denoising Using the Higher Order Singular Value Decomposition (2013, unknown): “The HOSVD is a generalization of the matrix SVD to higher order matrices [11].”
Adaptive blind signal and image processing (2002, background): “Like for adults, it would also be possible to measure the electrical activity of a fetal heart [726, 728].”
On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors (2001, methodology): “Finally, the HOPM can be viewed as a special case of the alternating least squares (ALS) iterative approach common in problems of multilinear model fitting (PARAFAC or CANDECOMP [18, 7, 27]) to multidimensional data.”
Orthogonal Tensor Decompositions (2000, methodology): “De Lathauwer [ 3 ] presents several ALS methods for computing the higher-order SVD.”
On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors (2000, background): “Multilinear algebra is gaining more and more interest, largely due to its applications in the context of higher-order statistics (HOS) [17, 18, 2, 4, 5, 7 ].”
Polytopic Decomposition of Linear Parameter-Varying Models by Tensor-Product Model Transformation (2006, unknown): “Petres Zoltán i”
Towards a standardized notation and terminology in multiway analysis (2000, background): “Note that the unit superdiagonal tensor should not to be denoted as ‘identity’, because it does not perform a role similar to that of the identity element (1) or matrix ( I ) in ordinary (matrix) algebra (see Reference [6], p. 26).”
Parallel factor analysis in sensor array processing (2000, methodology): “analysis has also been used in the context of higher order statistics (HOS)-based independent component analysis (ICA) of non-Gaussian source mixtures [10], [22].”
Multimodal Data Fusion: An Overview of Methods, Challenges, and Prospects (2015, unknown): “[84] L.”
Hyperspectral image noise reduction based on rank-1 tensor decomposition (2013, methodology): “Tensor (Lathauwer, 1997) and multilinear algebra have been receiving more and more attention and have recently been applied to both computer vision and pattern recognition (Lu et al., 2008; Shashua and Levin, 2001; Tao et al., 2007; Vasilescu and Terzopoulos, 2003).”
Mathematics in signal processing V (2003, methodology): “DeLathauwer’s PhD thesis [ 26 ] (1997); an interesting tool defined therein is the HOSVD [30] (DeLathauwer and others 1993), generalizing the concept of SVD to arrays of order 3, in a different manner compared to Carroll, but quite similar to the Tuckals decomposition [55] [68] [37] (Levin 1965; Tuc”
Numerical solution of the Hartree-Fock equation by multilevel tensor-structured methods (2011, methodology): “2 ([21]) Given a tensor A ∈ R1d and a matrix M ∈ Rll, we define the respective mode-l tensor-matrix product by B = A×l M ∈ R1l−1ll+1d, (2.”
A Multilinear Singular Value Decomposition (2000, methodology): “In [19] the HOSVD was used in a dimensionality reduction for higher-order factor analysis-type problems, reducing the computational complexity.”
Enhanced Line Search: A novel method to accelerate Parafac (2005, background): “It also finds applications in the signal processing area [11] [6] [7].”
Multilinear Wavelets: A Statistical Shape Space for Human Faces (2014, methodology): “The complexity of the HOSVD is O(d(2)1(d2d 2 3 + d3d 2 2)) [15], and we compute n of them.”