Nonseparable sparsity based hyperspectral compressive sensing

Accurate reconstruction of hyperspectral image(HSI) from a few random sampled measurements is crucial for hyperspectal compressive sensing. The underlying sparsity of HSI is one crucial factor for HSI reconstruction. However, the s-parsity is unknown in reality and varied with different noise. To address this problem, a novel nonseparable sparsity based hyperspectral compressive sensing(NSHCS) method is proposed in this study. We use empirical Bayes to deduce a non-separable sparsity constraint. The underlying correlation among sparse coefficients in signal is modeled implicitly by this sparsity constraint. Since parameters of this constraint are determined by the sampled measurements and the noise term together, the learned sparsity constraint can be adaptive to different noise. With this constraint, NSHCS can reconstruct the HSI precisely. Experimental results demonstrate the superiority of the proposed method over several state-of-the-art hyperspectral compressive sensing methods in HSI reconstruction.