A Scale-Invariant Relaxation in Low-Rank Tensor Recovery with an Application to Tensor Completion

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-03-29 DOI:10.1137/23m1560847

Huiwen Zheng, Yifei Lou, Guoliang Tian, Chao Wang

引用次数: 0

Abstract

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 756-783, March 2024.
Abstract. In this paper, we consider a low-rank tensor recovery problem. Based on the tensor singular value decomposition (t-SVD), we propose the ratio of the tensor nuclear norm and the tensor Frobenius norm (TNF) as a novel nonconvex surrogate of tensor’s tubal rank. The rationale of the proposed model for enforcing a low-rank structure is analyzed as its theoretical properties. Specifically, we introduce a null space property (NSP) type condition, under which a low-rank tensor is a local minimum for the proposed TNF recovery model. Numerically, we consider a low-rank tensor completion problem as a specific application of tensor recovery and employ the alternating direction method of multipliers (ADMM) to secure a model solution with guaranteed subsequential convergence under mild conditions. Extensive experiments demonstrate the superiority of our proposed model over state-of-the-art methods.

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低库张量恢复中的规模不变松弛，并应用于张量补全

SIAM 影像科学杂志》，第 17 卷第 1 期，第 756-783 页，2024 年 3 月。摘要本文考虑了一个低阶张量恢复问题。在张量奇异值分解（t-SVD）的基础上，我们提出了张量核规范和张量弗罗贝尼斯规范（TNF）的比值作为张量管秩的一种新的非凸代用指标。我们分析了所提出的强制低秩结构模型的理论依据。具体来说，我们引入了一个空空间属性（NSP）类型的条件，在该条件下，低阶张量是所提出的 TNF 恢复模型的局部最小值。在数值上，我们将低阶张量补全问题视为张量恢复的一个具体应用，并采用交替方向乘法（ADMM）来确保模型解在温和的条件下保证后续收敛。大量实验证明，我们提出的模型优于最先进的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Imaging Sciences COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

3.80

自引率

4.80%

发文量

审稿时长

>12 weeks

期刊介绍： SIAM Journal on Imaging Sciences (SIIMS) covers all areas of imaging sciences, broadly interpreted. It includes image formation, image processing, image analysis, image interpretation and understanding, imaging-related machine learning, and inverse problems in imaging; leading to applications to diverse areas in science, medicine, engineering, and other fields. The journal’s scope is meant to be broad enough to include areas now organized under the terms image processing, image analysis, computer graphics, computer vision, visual machine learning, and visualization. Formal approaches, at the level of mathematics and/or computations, as well as state-of-the-art practical results, are expected from manuscripts published in SIIMS. SIIMS is mathematically and computationally based, and offers a unique forum to highlight the commonality of methodology, models, and algorithms among diverse application areas of imaging sciences. SIIMS provides a broad authoritative source for fundamental results in imaging sciences, with a unique combination of mathematics and applications. SIIMS covers a broad range of areas, including but not limited to image formation, image processing, image analysis, computer graphics, computer vision, visualization, image understanding, pattern analysis, machine intelligence, remote sensing, geoscience, signal processing, medical and biomedical imaging, and seismic imaging. The fundamental mathematical theories addressing imaging problems covered by SIIMS include, but are not limited to, harmonic analysis, partial differential equations, differential geometry, numerical analysis, information theory, learning, optimization, statistics, and probability. Research papers that innovate both in the fundamentals and in the applications are especially welcome. SIIMS focuses on conceptually new ideas, methods, and fundamentals as applied to all aspects of imaging sciences.