Fast Grouped High-order SVD Method for Poisson Noise Removal in Video Sequential Images

High-order singular value decomposition (HOSVD) based low-rank tensor approximation has been successfully applied to high-dimensional data with multi-linear structures such as video sequential images and hyperspectral images. In some special imaging environments such as night vision surveillance, video images are usually seriously polluted by Poisson noise, but most current low-rank tensor approximation models only consider Gaussian noise. Moreover, due to the computational limitation of traditional SVD, HOSVD usually has low computational efficiency. In this paper, a low-rank and sparse regularization based tensor approximation model is proposed for Poisson noise removal in video sequential images. Considering diversity of image components in standard tensor unfoldings, we introduce a new multi-group nuclear norm based low-rank tensor prior in this new model which can be computed by grouped SVD. Using the technique of alternating direction method of multipliers(ADMM), we develop a fast parallel algorithm to solve the new model. Numerical results demonstrate our method is 9~10 times faster than traditional HOSVD method and can achieve similar or better results.