Orientation Invariant Tensor Completion In Both Spectual And Space Domains

The performance of most tensor completion algorithms heavily relies on the definition of tensor low-rankness. Among the various low-rank regularizations proposed in the last decade, the Tubal+Tucker Nuclear Norm (T2NN) firstly considers the low rankness both in spectral and space domains. However, this norm is unfortunately sensitive to the orientation, and thus fails to model low-rankness in multiple orientations. To this point, a new tensor norm, dubbed Orientation Invariant Hybrid Nuclear Norm (OIHNN), is first defined and then applied to formulate a new tensor completion model. To solve the model, an efficient algorithm is developed within the framework of Alternating Direction Method of Multipliers (ADMM). Effectiveness of our method is validated through experimental results on real datasets.

I. Introduction

In current big data era, tensors have applications in many fields, such as recommendation system [1], [2], seismic data reconstruction [3], and computer vision [4], because the acquisition, transmission and storage of data are in form of tensor. However, during these processes, the data may be missed, corrupted or polluted. So, it is necessary and important to recover the underlying tensor from its partially observed entries, or tensor completion.