Locally Similar Sparsity-Based Hyperspectral Compressive Sensing Using Unmixing

Linear unmixing-based compressive sensing has been extensively exploited for hyperspectral image (HSI) compression in recent years among which gradient sparsity is widely used to characterize the spatial continuity of abundance matrix given a small amount of endmembers. Though these methods have achieved good reconstruction results, identifying necessary endmembers from an HSI is challenging for them. In this study, instead of using a small amount of given endmembers, a locally similar sparsity-based hyperspectral unmixing compressive sensing (LSSHUCS) method is proposed to unmix the HSI with an established redundant endmember library. Considering that each pixel is a mixture of several endmembers, a novel locally similar sparsity constraint is imposed on the abundance matrix, which depicts the sparsity of abundance vectors and the local similarity among those sparse vectors simultaneously. This constraint guarantees to reconstruct the HSI precisely even with a quite low sample rate and can select the necessary endmembers from the endmember library automatically for unmixing. LSSHUCS is further extended to a more general one, which tactfully settles the spectrum variation problem, and an augmented Lagrangian algorithm is elaborated meticulously to solve the inverse linear problem in LSSHUCS. Extensive experimental results on both synthetic and real hyperspectral data demonstrate that the proposed method surpasses several state-of-the-art methods on reconstruction accuracy.