Temel Kavramlar
The core message of this work is to propose a novel tensor recovery model with learnable tensor nuclear norms to effectively address the non-smooth challenge in traditional t-SVD-based tensor recovery methods, and further develop a multi-objective tensor recovery framework to efficiently explore the low-rankness of tensor data across its various dimensions.
Özet
The content discusses the challenges faced by traditional t-SVD-based tensor recovery methods when dealing with tensor data exhibiting non-smooth changes, such as disordered image sequences and videos with rapidly changing frames. To address these issues, the authors introduce a novel tensor recovery model with a learnable tensor nuclear norm, which is solved using an Alternating Proximal Multiplier Method (APMM) algorithm.
The key highlights are:
- The proposed tensor recovery model incorporates learnable unitary matrices to effectively handle the non-smooth challenge caused by slice permutation variability and non-smooth changes in tensor data.
- The APMM algorithm is developed to solve the proposed tensor completion model, and its convergence to the Karush-Kuhn-Tucker (KKT) point is theoretically analyzed.
- A multi-objective tensor recovery framework is proposed to efficiently explore the low-rankness of tensor data across its various dimensions, without the need for introducing numerous tensor variables and weights as in traditional weighted sum-based methods.
- Extensive experiments on image and video inpainting tasks demonstrate the superior performance of the proposed methods compared to state-of-the-art tensor completion approaches, especially in scenarios involving non-smooth tensor data.
İstatistikler
The authors provide the following key figures and metrics to support their work:
Comparison of DFT-based and DCT-based t-SVD on the Yale dataset in ordered and randomly shuffled cases (Fig. 1)
Comparison of PSNR results by different tensor completion methods on the BSD dataset at various sampling rates (Table 2)
Comparison of PSNR results by different tensor completion methods on CIFAR10, CIFAR100, LFW, and GTF datasets at a sampling rate of 0.3 (Table 3)
Comparison of PSNR results by different tensor completion methods on 50 video segments from the HMDB51 dataset at a sampling rate of 0.3 (Fig. 4, Table 4)