Reconstruction of Hyperspectral Images from Spectral Compressed Sensing Based on a Multi-Type Mixing Model

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.