SIAM Journal on Scientific Computing· 2013Q1
An Order-$p$ Tensor Factorization with Applications in Imaging
- 316citations
- Q1SCImago
- 2013year
Short summary
A new order-p tensor factorization method, implemented using the Fast Fourier Transform for computational speed, is introduced for multiway data analysis.
AI-generated from the title and abstract; the full text is not read.
Key points
- Extends tensor factorization from order-3 to general order-p tensors.
- Implementation uses the Fast Fourier Transform for computational speed.
- Applications include image deblurring and video facial recognition (order-4 tensors).
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. SIAM Journal on Scientific Computing, 2013 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics