Low-Rank Tensor Recovery and Alignment Based on \(\ell _p\) Minimization

  • Kaifei Zhang
  • Di WangEmail author
  • Xiaoqin Zhang
  • Nannan Gu
  • Hongxing Jiang
  • Xiuzi Ye
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10116)


In this paper, we propose a framework of non-convex low-rank recovery and alignment for arbitrary tensor data. Specially, by using Schatten-p (\(0<p<1\), the same below) norm and \(\ell _p\) norm to relax the rank function and \(\ell _0\) norm respectively, the model requires much weaker incoherence conditions to guarantee a successful recovery than the common used nuclear norm and \(\ell _1\) norm. At the same time, we adopt a set of transformations which acts on the images of the tensor data to compensate the possible misalignments of images. By solving the optimal transformations, the strict alignments of the images are achieved in the low-rank recovery process. Furthermore, we propose an efficient algorithm based on the method of Alternating Direction Method of Multipliers (ADMM) for the non-convex optimization problem. The extensive experiments on the artificial data sets and real image data sets show the superiority of our method in image alignment and denoising.


Face Image Reconstruction Error Rank Function Pepper Noise Nuclear Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is supported by NSFC (Grants nos. 61305035, 61472285, 61511130084, and 61503263), Zhejiang Provincial Natural Science Foundation (Grants nos. LY17F030004, LR17F030001, LY16F020023, LY12F03016), Project of science and technology plans of Zhejiang Province (Grants nos. 2014C31062, 2015C31168). Project of science and technology plans of Wenzhou (Grants No. G20150017).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Kaifei Zhang
    • 1
  • Di Wang
    • 1
    Email author
  • Xiaoqin Zhang
    • 1
  • Nannan Gu
    • 2
  • Hongxing Jiang
    • 1
  • Xiuzi Ye
    • 1
  1. 1.College of Mathematics and Information ScienceWenzhou UniversityZhejiangChina
  2. 2.Capital University of Economics and BusinessBeijingChina

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