Dictionary Learning for Promoting Structured Sparsity in Hyperspectral Compressive Sensing

Abstract

The ability to accurately represent a hyperspectral image (HSI) as a combination of a small number of elements from an appropriate dictionary underpins much of the recent progress in hyperspectral compressive sensing (HCS). Preserving structure in the sparse representation is critical to achieving an accurate reconstruction but has thus far only been partially exploited because existing methods assume a predefined dictionary. To address this problem, a structured sparsity-based hyperspectral blind compressive sensing method is presented in this study. For the reconstructed HSI, a data-adaptive dictionary is learned directly from its noisy measurements, which promotes the underlying structured sparsity and obviously improves reconstruction accuracy. Specifically, a fully structured dictionary prior is first proposed to jointly depict the structure in each dictionary atom as well as the correlation between atoms, where the magnitude of each atom is also regularized. Then, a reweighted Laplace prior is employed to model the structured sparsity in the representation of the HSI. Based on these two priors, a unified optimization framework is proposed to learn both the dictionary and sparse representation from the measurements by alternatively optimizing two separate latent variable Bayes models. With the learned dictionary, the structured sparsity of HSIs can be well described by the reweighted Laplace prior. In addition, both the learned dictionary and sparse representation are robust to noise corruption in the measurements. Extensive experiments on three hyperspectral data sets demonstrate that the proposed method outperforms several state-of-the-art HCS methods in terms of the reconstruction accuracy achieved.