Hyperspectral compressed sensing (HCS) is a new imaging method that effectively reduces the power consumption of data acquisition. In this paper, we present a novel HCS algorithm by incorporating spatial-spectral hybrid compressed sensing, followed by a reconstruction based on spectral unmixing. At the sampling stage, the measurements are acquired by a spatial-spectral hybrid compressive sampling scheme to preserve the necessary information for the following spectral unmixing, where spatial compressive sampling mainly retains the endmember information, and spectral compressive sampling mainly retains the abundance information. Due to the limitations of the traditional linear mixed model (LMM), an improved mixed model is proposed for HCS reconstruction, which considers spectral variability, nonlinear mixing and other factors. At the reconstruction stage, based on the improved mixed model, semi-nonnegative matrix factorization (semi-NMF) is introduced to realize spectral unmixing on the measurements to achieve the final reconstruction by using an alternate iteration manner. The proposed algorithm is tested on real hyperspectral data and the selection of parameters is fully analyzed. Experimental results demonstrate that the proposed algorithm can significantly outperform state-of-the-art HCS algorithms in terms of reconstruction performance.

Hyperspectral compressed sensing (HCS) based on spectral unmixing technique has shown great reconstruction performance. In particular, the linear mixed model (LMM) has been widely used in HCS reconstruction. However, due to the complexity of environmental conditions, instrumental configurations, and material nonlinear mixing effects, LMM cannot accurately represent the hyperspectral images, which limits the improvement of reconstruction quality. In this article, first, by introducing spectral variability, nonlinear mixing, and residuals, a multitype mixed model (MMM) is proposed to establish a more accurate hyperspectral image model. Then, a novel MMM-based HCS is proposed, which performs spectral compressed sampling at the sampling stage only, and at the reconstruction stage, by using spectral unmixing, an MMM-based HCS super-resolution reconstruction algorithm from spectral compressed sensing data is developed, and the alternating direction multiplier method is employed to estimate each component of the MMM, furthermore, reasonable prior knowledge of each component is introduced to improve the estimation accuracy. Experimental results on hyperspectral datasets demonstrate that the proposed model outperforms those state-of-the-art methods based on the LMM in terms of HCS reconstruction quality. Index Terms-Compressed sensing, hyperspectral remote sensing, linear mixing model (LMM), spectral unmixing. I. INTRODUCTION H YPERSPECTRAL images (HSIs) can provide detailed ground features and are widely used in mineral exploration, agricultural production, environmental monitoring, and Manuscript

Compressed sensing is one of the key technologies to reduce the volume of hyperspectral image for real-time storage and transmission. Reconstruction based on spectral unmixing show tremendous potential in hyperspectral compressed sensing compared with other conventional algorithms that directly reconstruct images. In this paper, a joint spatial-spectral joint compressed sensing scheme is proposed. In this scheme, compressed hyperspectral data are collected by spatial-spectral hybrid compressed sampling. As for the reconstruction, an objective function is developed by introducing the fidelity constraints of spatial and spectral measurements and the row sparsity constraint of abundance that guarantee the precise reconstruction of hyperspectral images and obtain endmembers and abundances as by-products accurately. An augmented Lagrangian type algorithm is meticulously elaborated to solve the above optimization problem. Extensive experimental results on several real hyperspectral datasets indicate that the proposed approach can achieve a reconstruction accuracy higher than those of other state-of-the-art methods. The efficiency and feasibility of the proposed scheme give it great potential in hyperspectral compressed sensing.

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.