Hyperspectral Image Reconstruction via Block Low-Rank and Three-Dimension Weighted Total Variation Constraint

Compressed hyperspectral image reconstruction plays an important role in hyperspectral image processing, which aims to reduce the cost of transmission and recover the hyperspectral image from a small amount of data. Compressed sensing based methods have provided a new way for hyperspectral image reconstruction; however, the reconstruction problem is an ill-posed linear inverse problem, which needs some prior knowledge as constraint conditions. To make the most use of the prior knowledge, we introduce a block low-rank and three-dimension weighted total variation reconstruction algorithm. First, considering hyperspectral images have a piecewise smooth structure in both spatial and spectral domain, we use the total variation constraint in all three dimensions, and weight is utilized to trade off the contribution of the total variation in the different dimensions. Second, low-rank regularization is adopted in the reconstruction algorithm. To overcome the problem that the spectrum curves of different materials become similar which caused by the low-rank regular term, we divide the hyperspectral image into some non-overlapping blocks in the spatial domain and use low-rank regularization individually. Finally, taking into account the phenomenon that the rank of a block which has many elements in a given scene is usually higher than a normal block, we use one percent pixels in the original data to decide whether to perform low-rank constraint on the block or not. We use the fast iterative shrinkage/thresholding algorithm to solve the reconstruction problem. Extensive experiments demonstrate the superiority of the proposed model compared to other state-of-the-art reconstruction algorithms.