Robust tensor recovery with nonconvex and nonsmooth regularization

Shuang Zhang and Le Han

Applied Mathematics and Computation, 2023, vol. 438, issue C

Abstract: This paper considers the least squares loss minimization problem regularized by tensor average rank and zero norm, to decompose the noisy observation into a low-rank tensor, a sparse tensor and a noise tensor. Due to the nonconvex and nonsmooth of the average rank and the zero norm of tensors, it is not easy to solve the problem directly. We construct the variational characterizations of the tensor average rank and the tensor zero norm, get an equivalent mathematical program with an equilibrium constraint, and then propose an equivalent Lipschitz surrogate for the regularization problem by adding the equality constraint into the objective. Moreover, we design a convex algorithm with multi-stage to verify the efficiency of the proposed method. Numerical experiments are reported for simulation data and actual data to show the performance of the new method.

Keywords: Tensor average rank; Robust tensor recovery; Nonconvex; Nonsmooth (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:438:y:2023:i:c:s0096300322006403

DOI: 10.1016/j.amc.2022.127566

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