Generalized Dantzig Selector for Low-tubal-rank Tensor Recovery

Due to the superiority in exploiting the ubiquitous "spatial-shifting" property in modern multi-way data, the recently proposed low-tubal-rank model has been successfully applied for tensor recovery in signal processing and computer vision. In this paper, we define the generalized tensor Dantzig selector to recover a low-tubal-rank tensor from noisy linear measurements. Algorithmically, we develop an efficient algorithm based on the ADMM framework. Statistically, we establish non-asymptotic upper bounds on the estimation error for the problems of tensor completion and compressive sensing. Numerical experiments illustrate that our bounds can predict the scaling behavior of the estimation error. Experiments on realword datasets show the effectiveness of the proposed model.