Hyperspectral Compressed Sensing Reconstruction Applying Multi‐TV Collaboration

Abstract

For hyperspectral images (HSI) compressed sensing reconstruction, the 3D total variation (3DTV) is a powerful regulation term encoding the spatial-spectral local smooth prior structure. The term is calculated by supposing the sparsity structure on a gradient map along the spatial and spectral direction. In some real scenes, however, the gradient maps along different directions of HSI are not always sparse. Actually, TV constraints established on the gradient map of the original HSI are more effective in most cases. In this paper, instead of imposing sparsity on gradient maps themselves directly, compressed sensing (CS) reconstruction for HSI is formulated as an optimization problem utilizing a novel regulation term named multi-TV (MTV), which combines the sparsity prior for the gradient map and the TV projection along with other directions of the gradient map. We also develop a workable utility algorithm based on the alternating direction method of multipliers (ADMM) to effectively deal with the optimization problem. The proposed MTV term can easily replace the conventional 3DTV term and be embedded into hyperspectral CS (HCS) reconstruction to improve its performance. Experimental results show that compared with similar state-of-the-art methods, the proposed MTV term can significantly improve reconstruction precision for HCS.