Probability-weighted tensor robust PCA with CP decomposition for hyperspectral image restoration - Zhang, Aiyi; Liu, Fulai; Du, Ruiyan (Signal processing, 2023)
•Both sparse outliers and dense noise would affect the recovery performance of Hyperspectral Image.•Different weights could be imposed on the different components in Tensor robust principal component analysis (TRPCA) to further exploit their intrinsic property.•Soft-weight could be used to demonstrate the different effects of outliers and noise on data recovery from probability theory.•The weight could be effectively initialed by the prior knowledge, which is that outliers have a low occurrence probability.•TRPCA with CP decomposition would reduce computational complexity without losing rank information for data recovery. This paper presents a novel probability-weighted tensor robust principal component analysis (TRPCA) method based on CANDECOMP/PARAFAC decomposition (CPD) for hyperspectral image (HSI) restoration with low computational complexity from the coexistence of dense noise and sparse outliers. In the proposed method, via the CPD property, the tensor nuclear norm (TNN) optimization object is replaced as the CPD factor matrix of HSI with lower dimensions without losing low-rank property, so as to the computational complexity could be reduced during optimizing TNN in TRPCA model. To demonstrate the different effects of noise and outliers on HSI restoration, two weighted sets are defined with probability by the prior knowledge of the occurrence of outliers, which are used to analyze the probability whether the HSI is corrupted by dense noise or outliers. Via the probability theory, information entropy is employed to measure the uncertainty of noise and outlier occurrence in received data, so that to demonstrate their difference impacts on HSI restoration to improve the recovery accuracy. Theoretical analysis and simulation results show that the proposed method has lower computational complexity and better restoration performance compared with other related methods.