  Coded aperture snapshot spectral imaging (CASSI) is a promising technique to
capture the three-dimensional hyperspectral image (HSI) using a single coded
two-dimensional (2D) measurement, in which algorithms are used to perform the
inverse problem. Due to the ill-posed nature, various regularizers have been
exploited to reconstruct the 3D data from the 2D measurement. Unfortunately,
the accuracy and computational complexity are unsatisfied. One feasible
solution is to utilize additional information such as the RGB measurement in
CASSI. Considering the combined CASSI and RGB measurement, in this paper, we
propose a new fusion model for the HSI reconstruction. We investigate the
spectral low-rank property of HSI composed of a spectral basis and spatial
coefficients. Specifically, the RGB measurement is utilized to estimate the
coefficients, meanwhile the CASSI measurement is adopted to provide the
orthogonal spectral basis. We further propose a patch processing strategy to
enhance the spectral low-rank property of HSI. The proposed model neither
requires non-local processing or iteration, nor the spectral sensing matrix of
the RGB detector. Extensive experiments on both simulated and real HSI dataset
demonstrate that our proposed method outperforms previous state-of-the-art not
only in quality but also speeds up the reconstruction more than 5000 times.
