Low-rank Tensor Grid for Image Completion
arXiv:1903.04735
Abstract
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical ones. Compared with TT and TR, the projected entangled pair state (PEPS), which is also called tensor grid (TG), allows more interactions between different dimensions, and may lead to more compact representation. In this paper, we propose to perform image completion based on low-rank tensor grid. A two-stage density matrix renormalization group algorithm is used for initialization of TG decomposition, which consists of multiple TT decompositions. The latent TG factors can be alternatively obtained by solving alternating least squares problems. To further improve the computational efficiency, a multi-linear matrix factorization for low rank TG completion is developed by using parallel matrix factorization. Experimental results on synthetic data and real-world images show the proposed methods outperform the existing ones in terms of recovery accuracy.
References in corpus (19)
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Tensor Decomposition for Signal Processing and Machine Learning
- Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
- Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Parallel matrix factorization for low-rank tensor completion
- Spectral Unmixing via Data-guided Sparsity
- Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery
- Algorithms for finite Projected Entangled Pair States
- Era of Big Data Processing: A New Approach via Tensor Networks and Tensor Decompositions
- Provable Tensor Ring Completion
- Online Low-Rank Tensor Subspace Tracking from Incomplete Data by CP Decomposition using Recursive Least Squares
- Time evolution of projected entangled pair states in the single layer picture
- An Iterative Reweighted Method for Tucker Decomposition of Incomplete Multiway Tensors
- Tensor Completion by Alternating Minimization under the Tensor Train (TT) Model
- Tensor network ranks
- Learning Efficient Tensor Representations with Ring Structure Networks
- Higher-dimension Tensor Completion via Low-rank Tensor Ring Decomposition
- Beyond Unfolding: Exact Recovery of Latent Convex Tensor Decomposition under Reshuffling