Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimi-zation,need to pay an expensive computational cost due to multiple singular value decom-positions at each iteration.To overcome the drawback,we propose a scalable and efficient method,named parallel active subspace decomposition,which divides the unfolding along each mode of the tensor into a columnwise orthonormal matrix(active subspace)and another small-size matrix in parallel.Such a transformation leads to a nonconvex optimiza-tion problem in which the scale of nuclear norm minimization is generally much smaller than that in the original problem.We solve the optimization problem by an alternating direction method of multipliers and show that the iterates can be convergent within the given stopping criterion and the convergent solution is close to the global optimum solu-tion within the prescribed bound.Experimental results are given to demonstrate that the performance of the proposed model is better than the state-of-the-art methods.
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