Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm
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-ran...
| Authors | Shan Fan, Feng Zhang, Jianjun Wang et al. |
|---|---|
| Primary category | cs.CV |
| Published | 17 June 2026 |
| Last updated at source | 17 June 2026 |
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