Exploring Structured Sparsity by a Reweighted Laplace Prior for Hyperspectral Compressive Sensing

Abstract

Hyperspectral compressive sensing (HCS) can greatly reduce the enormous cost of hyperspectral images (HSIs) on imaging, storage, and transmission by only collecting a few compressive measurements in the image acquisition. One of the most challenging problems for HCS is how to reconstruct the HSI accurately from such a few measurements. It has been proved that introducing structure information into sparsity prior can improve the reconstruction performance of standard compressive sensing models. However, the structured sparsity of HSIs is unknown in reality and easily affected by random noise, which makes it difficult to explore the structured sparsity in HCS. To address this problem, we propose a novel reweighted Laplace prior-based HCS method in this paper. First, a hierarchical reweighted Laplace prior is proposed to model the distribution of sparsity in an HSI, which relieves the undemocratic penalization of traditional Laplace prior on nonzero coefficients of a sparse signal. Then, a latent variable-based Bayesian model is employed to learn the optimal configuration of the reweighted Laplace prior from the measurements. This model unifies signal recovery, sparsity prior learning, and noise estimation into a variational framework, where these three tasks are alternatively optimized till convergence. The finally learned sparsity prior can well represent the underlying structure in the sparse signal and is adaptive to the unknown noise. These advantages together improve the reconstruction accuracy of HCS obviously. Moreover, the proposed method is extended to learn a matrix normal distribution-based prior with a full covariance matrix, which depicts the underlying structure in the sparse signal better. As a result, the reconstruction accuracy is further improved. Extensive experimental results on three hyperspectral data sets demonstrate that the proposed method outperforms several state-of-the-art HCS methods in terms of the reconstruction accuracy.