Beyond Low Rank: A Graph-Based Propagation Approach to Tensor Completion for Multi-Acquisition Scenarios

Tensor completion refers to the problem of recovering the missing, corrupted or unobserved entries in data represented by tensors. In this paper, we tackle the tensor completion problem in the scenario in which multiple tensor acquisitions are available and do so without placing constraints on the underlying tensor's rank. Whereas previous tensor completion work primarily focuses on low-rank completion methods, we propose a novel graph-based diffusion approach to the problem. Referred to as GraphProp, the method propagates observed entries around a graph-based representation of the tensor in order to recover the missing entries. A series of experiments have been performed to validate the presented approach, including a synthetically-generated tensor recovery experiment which shows that the method can be used to recover both low and high rank tensor entries. The successful tensor completion capabilities of the approach are also demonstrated on a real-world completion problem from the field of multispectral remote sensing completion. Using data acquired from the Landsat 7 platform, we synthetically obscure image sections in order to simulate the scenario in which image acquisitions overlap only partially. In these tests, we benchmark against alternative tensor completion approaches as well as existing graph signal recovery methods, demonstrating the superior reconstruction performance of our method versus the state of the art.