Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers
Zhi-Yong Wang Hing Cheung So Abdelhak M. Zoubir
To alleviate the bias generated by the l1-norm in the low-rank tensor
completion problem, nonconvex surrogates/regularizers have been suggested to
replace the tensor nuclear norm, although both can achieve sparsity. However,
the thresholding functions of these nonconvex regularizers may not have
closed-form expressions and thus iterations are needed, which increases the
computational loads. To solve this issue, we devise a framework to generate
sparsity-inducing regularizers with closed-form thresholding functions. These
regularizers are applied to low-tubal-rank tensor completion, and efficient
algorithms based on the alternating direction method of multipliers are
developed. Furthermore, convergence of our methods is analyzed and it is proved
that the generated sequences are bounded and any limit point is a stationary
point. Experimental results using synthetic and real-world datasets show that
the proposed algorithms outperform the state-of-the-art methods in terms of
restoration performance.