High-order Tensor Completion for Data Recovery via Sparse Tensor-train Optimization
This work addresses the problem of recovering incomplete high-order tensor data, such as in image recovery, with incremental improvements in handling very high missing rates.
The paper tackles tensor data completion by proposing the Sparse Tensor-train Optimization (STTO) algorithm, which uses tensor-train decomposition and first-order optimization to recover incomplete data, achieving significantly better performance than state-of-the-art methods, especially at high missing rates of 90% to 99%.
In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train Optimization (STTO) which considers incomplete data as sparse tensor and uses first-order optimization method to find the factors of tensor-train decomposition. Our algorithm is shown to perform well in simulation experiments at both low-order cases and high-order cases. We also employ a tensorization method to transform data to a higher-order form to enhance the performance of our algorithm. The results of image recovery experiments in various cases manifest that our method outperforms other completion algorithms. Especially when the missing rate is very high, e.g., 90\% to 99\%, our method is significantly better than the state-of-the-art methods.