Tensor Robust Principal Component Analysis Via Non-Convex Double Logarithm-Type Penalty

In this thesis,we consider the tensor robust principal component analysis(TRPCA)problem,which aims to exactly recover the low-rank and sparse tensors from their sum.Different from current existing methods,we develop a novel tensor rank surrogate and a novel tensor sparsity surrogate as non-convex regularization to approximate the lowrank component and the sparse component,respectively.Based on these surrogates,we propose a non-convex double logarithm-type penalty.Equipped with the non-convex double logarithm-type penalty,we then solve the tensor robust principal component analysis problem by alternating direction method of multipliers(ADMM),and give its convergence analysis.Finally,numerical experiments from the image recovery and video foregroundbackground separation problems verify that our method outperforms the current existing methods.