An Inertial Proximal DC Algorithm for Low-Rank Tensor Completion

Abstract: Low-rank tensor completion based on tensor singular value decomposition (t-SVD) has
attracted considerable attention in recent years. Most existing methods adopt the
tensor nuclear norm (TNN) as a convex surrogate of the tensor tubal rank. However,
TNN imposes an identical penalty on all singular values, which may lead to excessive
shrinkage of large singular values and biased low-rank estimation. To alleviate this
limitation, we consider a nonconvex log-sum regularized tensor completion model
within the t-SVD framework. We exploit the difference-of-convex (DC) structure of the
objective function to derive a tractable proximal DC formulation. Based on this
formulation, an inertial proximal DC algorithm (IPDCA) with a restart strategy is
developed. Furthermore, the convergence of the generated sequence to a critical point
is established under the Kurdyka--\L ojasiewicz framework. Finally, numerical
experiments demonstrate the effectiveness of the proposed method.