Nonlocal tensor sparse representation and low-rank regularization for hyperspectral image compressive sensing reconstruction

Jize Xue, Yongqiang Zhao, Wenzhi Liao, Jonathan Cheung-Wai Chan

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28 Citations (Scopus)
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Hyperspectral image compressive sensing reconstruction (HSI-CSR) is an important issue in remote sensing, and has recently been investigated increasingly by the sparsity prior based approaches. However, most of the available HSI-CSR methods consider the sparsity prior in spatial and spectral vector domains via vectorizing hyperspectral cubes along a certain dimension. Besides, in most previous works, little attention has been paid to exploiting the underlying nonlocal structure in spatial domain of the HSI. In this paper, we propose a nonlocal tensor sparse and low-rank regularization (NTSRLR) approach, which can encode essential structured sparsity of an HSI and explore its advantages for HSI-CSR task. Specifically, we study how to utilize reasonably the l1 -based sparsity of core tensor and tensor nuclear norm function as tensor sparse and low-rank regularization, respectively, to describe the nonlocal spatial-spectral correlation hidden in an HSI. To study the minimization problem of the proposed algorithm, we design a fast implementation strategy based on the alternative direction multiplier method (ADMM) technique. Experimental results on various HSI datasets verify that the proposed HSI-CSR algorithm can significantly outperform existing state-of-the-art CSR techniques for HSI recovery.
Original languageEnglish
Article number193
Number of pages24
JournalRemote Sensing
Issue number2
Publication statusPublished - 19 Jan 2019


  • hyperspectral image
  • compressive sensing
  • structured sparsity
  • tensor sparse decomposition
  • tensor low-rank approximation

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