Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm
Researchers have introduced a new method for low-rank tensor completion (LRTC) that utilizes a novel nonconvex surrogate called the tensor nuclear norm to tensor Ky Fan p-k norm (TNPK). This approach aims to accurately approximate the tensor tubal rank and offers properties like scale invariance and parameter flexibility. The paper details a LRTC model and proves that low-rank tensors are local minimizers under specific conditions. An efficient algorithm, the alternating direction method of multipliers (ADMM), has been developed for this model, and experimental results show superior performance compared to existing methods. AI