Multishot Compressive Hyperspectral Imaging Based on Tensor Fibered Rank Minimization and Its Primal-Dual Algorithm

Coded aperture snapshot spectral imaging (CASSI) compresses tens to hundreds of spectral bands of the hyperspectral image (HSI) to a 2-D compressive measurement. For spatially or spectrally rich scenes, the compressive measurement provided by a single snapshot CASSI may not be sufficient. By taking multiple snapshots of the same scene, multishot CASSI leads to a less ill-posed inverse reconstruction problem, making the CASSI system more suitable for spatially or spectrally rich HSI. Considering the strong spectral correlation of HSI and the directional characteristics of mask shifting in multishot CASSI, the mode-1 tensor fibered rank (TFR) minimization is presented for its reconstruction in this article. Specifically, the mode-1 TFR is derived from the tensor singular value decomposition (t-SVD) to the mode-1 t-SVD, and the mode-1 TFR minimization is reduced to a mode-1 tensor nuclear norm minimization problem, to achieve more accurate HSI characterization in multishot CASSI reconstruction. The primal-dual algorithm (PDA) is applied to solve the objective optimization problem, which is flexible. Experimental results on the CAVE, Cuperite, and Urban datasets demonstrate the effectiveness of the proposed method.