Hyperspectral Image Completion Using Fully-Connected Extended Tensor Network Decomposition and Total Variation

The task of hyperspectral image completion generally involves random missing entries completion, stripes inpainting, and cloud removal, which can enhance the accuracy of subsequent image analysis. Recently, tensor completion has been presented for image recovery. Owing to the framelet basis redundancy, the tensor rank of the extended tensor via feature extraction is smaller, which can characterize the correlation between any two modes of the tensor more accurately. In this work, the fully connected tensor network decomposition has been suggested to depict the low-rankness of the extended tensor with feature extraction. The process of feature extraction via framelet transform reduces the need for fewer principal components to depict the low-rankness of the underlying tensor. Moreover, total variation is incorporated into the proposed completion model to capture the spatial smoothness of the underlying tensor via minimizing the sum of the gradients across the image. To solve the large-scale resulting model, the augmented Lagrange multiplier-based proximal alternating minimization algorithm has been proposed. To accelerate the optimization algorithm, the leverage score sampling and fast Fourier transform have been introduced. Numerical results on several types of hyperspectral image completion problem demonstrate that the proposed method performs better than the compared methods in data completion.