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An Order- $p$Tensor Factorization with Applications in Imaging
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Journal Article
An Order- $p$Tensor Factorization with Applications in Imaging
2013
Overview
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]
Publisher
Society for Industrial and Applied Mathematics
Subject
