  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.
