Recovering orthogonal tensors under arbitrarily strong, but locally correlated, noise

We consider the problem of recovering an orthogonally decomposable tensor with a subset elements distorted by noise arbitrarily large magnitude. focus on particular case where each mode in decomposition is corrupted vectors components that are correlated locally, i.e., nearby components. show this deterministic completion has unusual property it can be solved polynomial time if rank sufficiently large. This polar opposite low-rank assumptions typical and matrix settings. our through system coupled Sylvester-like equations how to accelerate their solution alternating solver. enables recovery even substantial number missing entries, for instance $n$-dimensional tensors $n$ up $40\%$ entries.