PaperActive

Semi-Tensor Product-Based Multi-Term Randomized T-SVD and Its Visual Applications

Updated 4 h ago · first seen 11 Sept 2026

paper_01M294FP2K9NXCGVQSG57H3HP6

Published: 11 Sept 2026; T1 · 4 h ago
arXiv: 2609.11168; T1 · 4 h ago
Category: cs.LG; T1 · 4 h ago

Abstract

Tensor singular value decomposition (T-SVD), which is built upon the tensor-tensor product (t-product), has emerged as a powerful tool for processing high-dimensional visual data such as color images and videos. However, the standard t-product imposes strict dimensional compatibility constraints. Although extensions based on the semi-tensor product (STP) relax this restriction, their single-term formulations still suffer from limited approximation accuracy. Moreover, these deterministic methods incur high computational costs when processing large-scale tensor data. To address these issues, this paper introduces a novel semi-tensor product for third-order tensors under the t-product framework induced by arbitrary invertible linear transforms. The resulting tensor semi-tensor product breaks the rigid dimension matching requirement of the standard t-product, while retaining the closed-form property of T-SVD. Based on this construction, we develop a multi-term semi-tensor product singular value decomposition (MSTP-SVD), which integrates multiple orthogonal decomposition terms to significantly improve low-rank approximation accuracy compared with single-term schemes. To reduce the computational cost of multi-term modeling, we incorporate randomized projection and power iteration techniques into the MSTP-SVD framework, yielding an accelerated multi-term randomized semi-tensor product SVD (MRSTP-SVD) algorithm that achieves a balance between reconstruction accuracy and computational efficiency. Experiments on image and video compression and completion tasks demonstrate the effectiveness of the proposed method.

Authors 8

Xingchen Xiao (School of Mathematics, Statistics, Southwest University, Chongqing, China), Feng Zhang (School of Mathematics, Wenjin Qin (School of Mathematics, Jianjun Wang (School of Mathematics

Specification

Official page: arxiv.org/abs/2609.11168
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Arxiv announce type: new
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
arXiv id: 2609.11168
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Categories: cs.LG
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
PDF: arxiv.org/pdf/2609.11168
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh

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T19

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4 h ago

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9 claims · 9 properties

Official pageofficial_url1

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https://arxiv.org/abs/2609.11168	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Abstractabstract1

Claim history for Abstract
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Tensor singular value decomposition (T-SVD), which is built upon the tensor-tensor product (t-product), has emerged as a powerful tool for processing high-dimensional visual data such as color images and videos. However, the standard t-product imposes strict dimensional compatibility constraints. Although extensions based on the semi-tensor product (STP) relax this restriction, their single-term formulations still suffer from limited approximation accuracy. Moreover, these deterministic methods incur high computational costs when processing large-scale tensor data. To address these issues, this paper introduces a novel semi-tensor product for third-order tensors under the t-product framework induced by arbitrary invertible linear transforms. The resulting tensor semi-tensor product breaks the rigid dimension matching requirement of the standard t-product, while retaining the closed-form property of T-SVD. Based on this construction, we develop a multi-term semi-tensor product singular value decomposition (MSTP-SVD), which integrates multiple orthogonal decomposition terms to significantly improve low-rank approximation accuracy compared with single-term schemes. To reduce the computational cost of multi-term modeling, we incorporate randomized projection and power iteration techniques into the MSTP-SVD framework, yielding an accelerated multi-term randomized semi-tensor product SVD (MRSTP-SVD) algorithm that achieves a balance between reconstruction accuracy and computational efficiency. Experiments on image and video compression and completion tasks demonstrate the effectiveness of the proposed method.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Arxiv announce typearxiv_announce_type1

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new	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

arXiv idarxiv_id1

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2609.11168	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Authorsauthors1

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Xingchen Xiao (School of Mathematics, Statistics, Southwest University, Chongqing, China), Feng Zhang (School of Mathematics, Wenjin Qin (School of Mathematics, Jianjun Wang (School of Mathematics	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Categoriescategories1

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cs.LG	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

PDFpdf_url1

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https://arxiv.org/pdf/2609.11168	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Primary categoryprimary_category1

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cs.LG	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Publishedpublished_at1

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11 Sept 2026	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	4 h ago	1

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