An Order-$p$ Tensor Factorization with Applications in Imaging

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....

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 35; no. 1; pp. A474 - A490
Main Authors: Martin, Carla D., Shafer, Richard, LaRue, Betsy
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects:
Algorithms
Applied mathematics
Arrays
Computation
Data analysis
Decomposition
Face recognition
Factorization
Fourier transforms
Imaging
Linear algebra
Mathematical analysis
Strategy
Tensors
ISSN:1064-8275, 1095-7197
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. [PUBLICATION ABSTRACT]
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ObjectType-Article-2
ObjectType-Feature-1
content type line 23
ISSN:1064-8275
1095-7197
DOI:10.1137/110841229