title: Manifold regularization for sparse unmixing of hyperspectral images.
abstract: BACKGROUND
  Recently,sparse unmixinghas 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 ascollaborative sparse regression, ignore the intrinsic geometric structure in the hyperspectral data.
  
  
  RESULTS
  In this paper, we propose a novel model, calledmanifold 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 onalternating direction method of multipliershas 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.
authors.affiliation: School of Mathematics and Statistics, Xi'an Jiaotong University, Xianning West Road, Xi'an, 710049 China.
authors.forename: Junmin
authors.initials: J
authors.lastname: Liu
authors.affiliation: School of Mathematics and Statistics, Xi'an Jiaotong University, Xianning West Road, Xi'an, 710049 China.
authors.forename: Chunxia
authors.initials: C
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Statistics, Xi'an Jiaotong University, Xianning West Road, Xi'an, 710049 China.
authors.forename: Jiangshe
authors.initials: J
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Statistics, Xi'an Jiaotong University, Xianning West Road, Xi'an, 710049 China.
authors.forename: Huirong
authors.initials: H
authors.lastname: Li
authors.affiliation: School of Information and Computing Science, Beifang University of Nationalities, Wenchang North Road, Yinchuan, 750021 China.
authors.forename: Yuelin
authors.initials: Y
authors.lastname: Gao
keywords: Hyperspectral images; Manifold regularization; Spectral unmixing