The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
An Order-$p$ Tensor Factorization with Applications in Imaging
Abstract
Operations with tensors, or multiway arrays, are increasingly prevalent in many applications involving multiway data analysis. This paper extends a third-order factorization strategy and tensor operations defined in a recent paper [M. E. Kilmer and C. D. Martin, Linear Algebra Appl., 435 (2011), pp. 641--658] to order-$p$ tensors. The extension to order-$p$ tensors is explained in a recursive way but for computational speed is implemented directly using the fast Fourier transform. A major motivation for considering factorization strategies for order-$p$ tensors is to devise new types of algorithms for general order-$p$ tensors which can be used in applications. We conclude with two applications in imaging. The first application is image deblurring, and the second application is video facial recognition. Both applications involve order-4 tensors.
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Cites
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Tensor Decompositions and Applications
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A Multilinear Singular Value Decomposition
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Factorization strategies for third-order tensors
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Self-citationConjugate Gradient Methods for Toeplitz Systems
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Decomposing EEG data into space–time–frequency components using Parallel Factor Analysis
Miwakeichi, F., Martı́nez-Montes, E., Valdés-Sosa, P. A., Nishiyama, N., Mizuhara, H., & Yamaguchi, Y. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2004.03.039 · Cited by 374
Concurrent EEG/fMRI analysis by multiway Partial Least Squares
Martı́nez-Montes, E., Valdés-Sosa, P. A., Miwakeichi, F., Goldman, R. I., & Cohen, M. S. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2004.03.038 · Cited by 326
Metadata
- Authors
- Martin, C. D., Shafer, R., & LaRue, B.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2013-01
- Volume
- 35
- Issue
- 1
- Pages
- A474-A490
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2000015923
- Cited by
- 296
- References
- 11
- FWCI
- 1.56
- Type
- journal article
- Language
- en
- Open access
- closed
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