An Order-p Tensor Factorization with Applications in Imaging

By Carla D. Moravitz Martin, Ricky D. Shafer, Betsy LaRue. SIAM Journal on Scientific Computing, 2013

314 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mathematics

View Paper: https://www.semanticscholar.org/paper/8514f5a168c16d4012de241400b12a1966e42cc6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jiashi Feng
2. Shuicheng Yan
3. Pan Zhou
4. Zhouchen Lin
5. Canyi Lu
6. Wei David Liu
7. Yudong Chen
8. Yimin Wei

In Computational Mathematics

1. Yimin Wei
2. Liqun Qi
3. Yun Miao
4. Zhouchen Lin
5. Canyi Lu
6. Shuchin Aeron
7. Misha Elena Kilmer
8. Wei David Liu

Citations in the corpus

• Tensor-Tensor Products with Invertible Linear Transforms (2015, unknown): “Recently, the t-product has been introduced as a useful generalization of matrix multiplication for tensors of order three (i.e. three-way arrays) [1] and higher [2].”
• Generalized tensor function via the tensor singular value decomposition based on the T-product (2019, methodology): “tries are in R and a tensor is a complex tensor if all its entries are in C. Recently, the tensor T-product has been established and proved to be a useful tool in many areas, such as image processing [28, 29, 42, 47, 50, 60], computer vision [4, 17, 53, 55], signal processing [10, 34, 37, 48], low r”
• 5D seismic data completion and denoising using a novel class of tensor decompositions (2015, methodology): “Kilmer and Martin (2011a) develop tSVD for third-order tensors and Martin et al. (2013) extend it to higher orders.”
• Novel Methods for Multilinear Data Completion and De-noising Based on Tensor-SVD (2014, methodology): “-SVD is based on an operator theoretic interpretation of third-order tensors as linear operators on the space of oriented matrices [2]. This notion can be extended recursively to higher order tensors [16]. In this paper we will exploit this decomposition, the associated notion of tensor multi-rank a”
• Tensor Factorization for Low-Rank Tensor Completion (2018, background): “However, as pointed out by [32], [33], [36], and [37], directly unfolding a tensor would destroy the original multi-way structure of the data, leading to vital information loss and degraded performance.”
• T-Jordan Canonical Form and T-Drazin Inverse Based on the T-Product (2019, background): “he outer inverse by Einstein product is developed by Stanimirovic et al. [56] The tensor T-product introduced by Kilmer [34] has been proved to be of great use in many areas, such as image processing [33, 34, 49, 55, 59, 70], computer vision [20, 64], signal processing [12, 41, 44, 58], low rank ten”
• Exact Tensor Completion Using t-SVD (2015, methodology): “One can obtain this decomposition by computing matrix SVDs in the Fourier domain, see Algorithm 1, where the the algorithm is given for a general order N tensor, obtained by recursively applying the Fourier transform over successive dimensions [26].”
• Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm (2018, methodology): “2 was given first in [14] and later in some other related works [10], [21].”
• Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization (2016, methodology): “1 to the case of order-p (p ≥ 3) tensors, by using the t-SVD for order-p tensors in [19].”