Manifold regularization for sparse unmixing of hyperspectral images

Background: Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression, ignore the intrinsic geometric structure in the hyperspectral data. Results: In this paper, we propose a novel model, called manifold regularized collaborative sparse regression, by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model. Conclusions: Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.