Tensor Compressive Sensing Fused Low-Rankness and Local-Smoothness

A plethora of previous studies indicates that making full use of multifarious intrinsic properties of primordial data is a valid pathway to recover original images from their degraded observations. Typically, both low-rankness and local-smoothness broadly exist in real-world tensor data such as hyperspectral images and videos. Modeling based on both properties has received a great deal of attention, whereas most studies concentrate on experimental performance, and theoretical investigations are still lacking. In this paper, we study the tensor compressive sensing problem based on the tensor correlated total variation, which is a new regularizer used to simultaneously capture both properties existing in the same dataset. The new regularizer has the outstanding advantage of not using a trade-off parameter to balance the two properties. The obtained theories provide a robust recovery guarantee, where the error bound shows that our model certainly benefits from both properties in ground-truth data adaptively. Moreover, based on the ADMM update procedure, we design an algorithm with a global convergence guarantee to solve this model. At last, we carry out experiments to apply our model to hyperspectral image and video restoration problems. The experimental results show that our method is prominently better than many other competing ones. Our code and Supplementary Material are available at https://github.com/fsliuxl/cs-tctv.