Third-Order Tensors as Linear Operators on a Space of Matrices

By Karen S. Braman. 2010

249 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2afc2e5d1060b89b58129d4b3edd81021844d130

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In Computational Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Novel Methods for Multilinear Data Completion and De-noising Based on Tensor-SVD (2014, methodology): “Section 2 presents the notations and provide an overview and key results on tSVD from [2, 12, 11] and illustrates the key differences and advantages over other tensor decomposition methods.”
5D seismic data completion and denoising using a novel class of tensor decompositions (2015, methodology): “To define the 3D tensor as a linear operator on the set of oriented matrices ~M, Braman (2010) defines a commutative multiplication operation between two tubes ~v ∈ R1×1×n3 and ~u ∈ R1×1×n3 resulting in another tube of same length.”
Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging (2013, methodology): “We note that an alternative is to adopt the conventions in the paper [2], adjusted for dimension.”
Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization (2016, background): “More recently, the work [28] proposes the tensor tubal rank based on a new tensor decomposition scheme in [2, 14], which is referred as tensor SVD (t-SVD).”
Tensor-Tensor Products with Invertible Linear Transforms (2015, methodology): “…reader that because of this one-to-one relationship between elements of K mn and C m n , we will refer to elements of K mn also as In the spirit of [8], the set of oriented matrices can thus be thought of as a module over the ring K n , i.e. a space where the scalars are tube ﬁbers in K n instead…”