ITERATIVE SINGULAR TUBE HARD THRESHOLDING ALGORITHMS FOR TENSOR RECOVERY

Rachel Grotheer; Shuang Li; Anna Ma; Deanna Needell; Jing Qin

doi:10.3934/ipi.2023059

ITERATIVE SINGULAR TUBE HARD THRESHOLDING ALGORITHMS FOR TENSOR RECOVERY

Rachel Grotheer, Shuang Li, Anna Ma, Deanna Needell, Jing Qin

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be further used to define the best low-rank approximation of a tensor to significantly reduce the dimensionality for signal compression and recovery. In this paper, we consider the low-rank tensor recovery problem when the tubal rank of the underlying tensor is given or estimated a priori. We propose a novel class of iterative singular tube hard thresholding algorithms for tensor recovery based on the low-tubal-rank tensor approximation, including basic, accelerated deterministic and stochastic versions. Convergence guarantees are provided along with the special case when the measurements are linear. Numerical experiments on tensor compressive sensing and color image inpainting are conducted to demonstrate convergence and computational efficiency in practice.

Original language	English
Pages (from-to)	889-907
Number of pages	19
Journal	Inverse Problems and Imaging
Volume	18
Issue number	4
DOIs	https://doi.org/10.3934/ipi.2023059
State	Published - Aug 2024

Bibliographical note

Publisher Copyright:
© 2024, American Institute of Mathematical Sciences. All rights reserved.

Funding

Acknowledgments. This material is based upon work supported by the National Security Agency under Grant No. H98230-19-1-0119, The Lyda Hill Foundation, The McGovern Foundation, and Microsoft Research, while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the summer of 2019. In addition, Grotheer was supported by the Goucher College Summer Research grant, Needell was funded by NSF CAREER DMS #2011140 and NSF DMS #2108479, and Qin is supported by NSF DMS #1941197.

Funders	Funder number
McGovern Foundation
Lyda Hill Foundation
Microsoft Research
National Security Agency	H98230-19-1-0119
National Science Foundation Arctic Social Science Program	2011140
Division of Mathematical Sciences	1941197, 2108479

Keywords

Tensor completion
hard thresholding
image inpainting
stochastic algorithm
tubal rank

ASJC Scopus subject areas

Analysis
Modeling and Simulation
Discrete Mathematics and Combinatorics
Control and Optimization

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10.3934/ipi.2023059

Cite this

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title = "ITERATIVE SINGULAR TUBE HARD THRESHOLDING ALGORITHMS FOR TENSOR RECOVERY",

abstract = "Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be further used to define the best low-rank approximation of a tensor to significantly reduce the dimensionality for signal compression and recovery. In this paper, we consider the low-rank tensor recovery problem when the tubal rank of the underlying tensor is given or estimated a priori. We propose a novel class of iterative singular tube hard thresholding algorithms for tensor recovery based on the low-tubal-rank tensor approximation, including basic, accelerated deterministic and stochastic versions. Convergence guarantees are provided along with the special case when the measurements are linear. Numerical experiments on tensor compressive sensing and color image inpainting are conducted to demonstrate convergence and computational efficiency in practice.",

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AU - Needell, Deanna

AU - Qin, Jing

PY - 2024/8

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AB - Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be further used to define the best low-rank approximation of a tensor to significantly reduce the dimensionality for signal compression and recovery. In this paper, we consider the low-rank tensor recovery problem when the tubal rank of the underlying tensor is given or estimated a priori. We propose a novel class of iterative singular tube hard thresholding algorithms for tensor recovery based on the low-tubal-rank tensor approximation, including basic, accelerated deterministic and stochastic versions. Convergence guarantees are provided along with the special case when the measurements are linear. Numerical experiments on tensor compressive sensing and color image inpainting are conducted to demonstrate convergence and computational efficiency in practice.

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KW - image inpainting

KW - stochastic algorithm

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ITERATIVE SINGULAR TUBE HARD THRESHOLDING ALGORITHMS FOR TENSOR RECOVERY

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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