Hierarchical Low-Rank Model with Double Tensor Structural Sparsity for Tensor Completion

In the field of tensor completion, existing models employing a mono-layered low-rank structure have exhibited potent results. For comprehensive exploitation of tensor data's intrinsic low-rankness, a novel hierarchical low-rank model that amalgamates double tensor structural sparsity is presented, specifically devised for the completion of third-order tensors. This innovative model concurrently encapsulates the initial-layer low-rankness derived from the primal tensor objects, facilitated by means of tensor factorization via the t-product. Further, the low-rankness of each constituent factor tensor at the secondary layer is characterized employing an innovative tensor structural sparsity regularizer. The model is further fortified by a surrogate theorem, ostensibly asserting that the aforementioned hierarchical low-rank model can offer a more precise representation of tensor multi-rank. Additionally, an efficient learning algorithm for the model has been developed. Comprehensive experimental results exhibit the hierarchical low-rank model's superiority over competing methods of tensor completion that merely consider mono-layered low-rankness.