Low-rank tensor recovery via non-convex regularization, structured factorization and spatio-temporal characteristics

Abstract

Recently, the convex low-rank 3rd-order tensor recovery has attracted considerable attention. However, there are some limitations to the convex relaxation approach, which may yield biased estimators. To overcome this disadvantage, we develop a novel non-convex tensor pseudo-norm to replace the weighted sum of the tensor nuclear norm as a tighter rank approximation. Then in tensor robust principle component analysis, we introduce the noise analysis to separate the spare foreground from the dynamic background more accurately. Furthermore, by introducing a spatio-temporal matrix, we can make better use of the inherent spatio-temporal characteristics of the low-rank static background and sparse foreground. Finally, we introduce an incoherent term to constrain the sparse foreground and the dynamic background to improve the separability. Some preliminary numerical examples of color image, video, and face image data sets are presented to illustrate the efficiency of our proposed methods.