Optimal Low-Rank Tensor Tree Completion

Tensor completion is a powerful technique for recovering missing entries from partial observations. Tensor tree network, with a hierarchical structure, has gained widespread attention for its ability to balance and effectively explore the correlations in high-order data. However, the performance of tensor trees is influenced by the order of modes, leading to variations in their effectiveness. To address this, we propose to minimize the loss of entanglement entropy to determine the optimal mode order within the tensor tree network, thereby optimizing its representation performance. We correspondingly construct an optimal low-rank tensor tree completion model, where the optimal low-rank tensor tree network captures global structures and total variation investigates local structures. The alternating direction method of multipliers is employed to solve the optimization problem. Experimental results on color images and light field images demonstrate that our method outperforms state-of-the-art algorithms in terms of recovery performance.