Generalized Nonconvex Approach for Low-Tubal-Rank Tensor Recovery. Academic Article uri icon


  • The tensor-tensor product-induced tensor nuclear norm (t-TNN) (Lu et al., 2020) minimization for low-tubal-rank tensor recovery attracts broad attention recently. However, minimizing the t-TNN faces some drawbacks. For example, the obtained solution could be suboptimal to the original problem due to its loose approximation. In this article, we extract a unified nonconvex surrogate of the tensor tubal rank as a tighter regularizer, which involves many popular nonconvex penalty functions. An iterative reweighted t-TNN algorithm is proposed to solve the resulting generalized nonconvex tubal rank minimization for tensor recovery. It converges to a critical point globally with rigorous proofs based on the Kurdyka-ojasiwicz property. Furthermore, we provide the theoretical guarantees for exact and robust recovery by developing the tensor null space property. Extensive experiments demonstrate that our approach markedly enhances recovery performance compared with several state-of-the-art convex and nonconvex methods.

published proceedings

  • IEEE Trans Neural Netw Learn Syst

author list (cited authors)

  • Wang, H., Zhang, F., Wang, J., Huang, T., Huang, J., & Liu, X.

citation count

  • 5

complete list of authors

  • Wang, Hailin||Zhang, Feng||Wang, Jianjun||Huang, Tingwen||Huang, Jianwen||Liu, Xinling

publication date

  • August 2022