Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm

• URL: http://arxiv.org/abs/2606.19046v1
• Date: Wed, 17 Jun 2026 13:12:07 GMT
• Title: Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm
• Abstract summary: This paper addresses low-rank tensor completion (LRTC)<n>It proposes a novel non surrogate, namely the ratio of the tub tensor norm to the tensor Ky Fan p-k norm (TNK)
• Score: 63.91066367247722
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper addresses low-rank tensor completion (LRTC) by proposing a novel nonconvex surrogate, namely the ratio of the tensor nuclear norm to the tensor Ky Fan p-k norm (TNPK), to accurately approximate the tensor tubal rank. The TNPK possesses appealing properties, including scale invariance, parameter flexibility, and the existence of closed-form solutions under specific choices of p and k. With specific parameter settings of p and k, it reduces to the ratio of the tensor nuclear norm to the tensor Ky Fan k norm (TNK) or the ratio of the tensor nuclear norm to the tensor Frobenius norm (TNF). We construct a LRTC model and, under the tensor null space property (NSP), prove that low-rank tensors are local minimizers of the proposed model. Moreover, we derive the proximal operator of the Ky Fan p-k inverse-norm and further develop an efficient alternating direction method of multipliers (ADMM) algorithm with guaranteed subsequential convergence under mild conditions. Extensive experiments on synthetic and real-world datasets validate the superior performance of our method against state-of-the-art competitors.

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