Total variation regularized nonlocal low-rank tensor train for spectral compressive imaging

Abstract

In this paper, we consider the reconstruction problem of hyperspectral images (HSIs) based on a new type of imaging system termed as coded aperture snapshot spectral imaging (CASSI). CASSI compresses multiple spectral bands of HSI into a single snapshot measurement which enjoys low cost, low bandwidth, and high-speed sensing rate. Despite the promising applications of CASSI systems, the bottleneck lies in the reconstruction algorithms. The existing CASSI reconstruction methods could not fully exploit the underlying structures of HSIs, and thereby demonstrate unsatisfactory reconstruction quality. To remedy this issue, we propose in this paper a novel tensor-based method by modeling two intrinsic HSI priors, namely nonlocal low-rank tensor train (NLTT) and 3-D weighted total variation (3DWTV). Taking into consideration that the snapshot measurement and targeted HSI should share similar spatial structures, we use the snapshot measurement to help group nonlocal spatially similar cubes within the unknown HSI to form 4-D tensors. And the NLTT prior employed on these 4-D tensors can effectively learn the correlations among the spatial, spectral and nonlocal modes thanks to the well-balanced matricization scheme of TT rank. Meanwhile, we employ the 3DWTV prior to characterize the local smoothness of the spatial and spectral modes. The resulting model can be solved efficiently by using the alternative direction method of multipliers (ADMM). Extensive experiments on both simulated and real CASSI datasets validate the improved reconstruction performance of our method over several other competing ones.