Adaptive Weighted Robust Data Recovery with Total Variation for Hyperspectral Image

This paper proposes an adaptive weighted robust data recovery method with total variation (TV) regularization for hyperspectral image (HSI). In the proposed method, the HSI recovery problem is modeled as a tensor robust principal component analysis optimization problem, which decomposes the received data into low-rank HSI data, outliers, and noise component, with tensor nuclear norm (TNN), ℓ1 norm, and ℓF norm constrained, respectively. Then, an adaptive weighted strategy is defined to impose on the TNN and outliers to flexibly use the priori information of singular values (SVs) and strengthen the sparsity of outliers, where the weights are adaptively conducted by the elements in SVs and outliers. Specifically, the weighted strategy in TNN retains larger SVs to determine the main information for data recovery, while penalizing smaller SVs to eliminate the influence of interference. And the weighted strategy on outliers enables the proposed method to more effectively measure the sparsity of outliers. Furthermore, TV regularization is introduced to extract the local information for data recovery by a difference operation along different modes, which also can help the proposed method avoid the detail loss caused by the weighted strategy. Experiments confirm that the proposed method significantly outperforms the existing methods.