Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm

Tai-Xiang Jiang, Ting-Zhu Huang, Xi-Le Zhao, Liang-Jian Deng
12/15/2017
math.NAcs.CV

Official code: TaiXiangJiang/PSTNN (6 stars, last commit 2025-12-03).

Abstract

In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal multi-rank. We build two PSTNN-based minimization models for two typical tensor recovery problems, i.e., the tensor completion and the tensor principal component analysis. We give two algorithms based on the alternating direction method of multipliers (ADMM) to solve proposed PSTNN-based tensor recovery models. Experimental results on the synthetic data and real-world data reveal the superior of the proposed PSTNN.

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Code Implementations(1)

TaiXiangJiang/PSTNNOfficial100%

PSTNN code

64MATLABMar 21, 201810 months ago

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Cite this paper

@article{jiang2017multidimensional,
  title  = {Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm},
  author = {Tai-Xiang Jiang and Ting-Zhu Huang and Xi-Le Zhao and Liang-Jian Deng},
  year   = {2017},
  eprint = {1712.05870},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1712.05870}
}

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