  Tensor sparse modeling as a promising approach, in the whole of science and
engineering has been a huge success. As is known to all, various data in
practical application are often generated by multiple factors, so the use of
tensors to represent the data containing the internal structure of multiple
factors came into being. However, different from the matrix case, constructing
reasonable sparse measure of tensor is a relatively difficult and very
important task. Therefore, in this paper, we propose a new tensor sparsity
measure called Tensor Full Feature Measure (FFM). It can simultaneously
describe the feature information of each dimension of the tensor and the
related features between two dimensions, and connect the Tucker rank with the
tensor tube rank. This measurement method can describe the sparse features of
the tensor more comprehensively. On this basis, we establish its non-convex
relaxation, and apply FFM to low rank tensor completion (LRTC) and tensor
robust principal component analysis (TRPCA). LRTC and TRPCA models based on FFM
are proposed, and two efficient Alternating Direction Multiplier Method (ADMM)
algorithms are developed to solve the proposed model. A variety of real
numerical experiments substantiate the superiority of the proposed methods
beyond state-of-the-arts.
