NOISY TENSOR COMPLETION VIA ORIENTATION INVARIANT TUBAL NUCLEAR NORM

Noisy tensor completion is considered for reconstructing multi-way data from a small fraction of noisy observations caused by many practical reasons such as sensor dead pixels, communication loss, electromagnetic interferences, etc., and can provide a powerful pre-processing tool for subsequent tasks like classification, unmixing, and target detection in many remote sensing applications. Thanks to the capability to simultaneously model multi-orientational spectral low-rankness, the recently proposed Orientation Invariant Tubal Nuclear Norm (OITNN) empirically outperforms traditional tensor nuclear norms in tensor recovery tasks. However, its theoretical and empirical performance for noisy tensor completion is still insufficiently explored. To further unleash and understand the modeling potential of OITNN, this paper formulates an OITNN penalized least squares estimator for noisy tensor completion and studies its statistical and empirical performance. We compute the proposed estimator using an ADMM-based algorithm and rigorously characterize the statistical performance by establishing an upper bound on the estimation error. Simulation studies on nine different types of remote sensing data demonstrate the effectiveness of the OITNN for noisy tensor completion.