Spatial-spectral sparse unmixing for hyperspectral imagery based on graph Laplacian

Abstract

Aiming at improving the accuracy of unmixing result, this paper proposes an unmixing model for hyperspectral imagery which utilize both spatial and spectral information. A spatial-spectral sparse constraint unmixing algorithm based on Graph Laplacian (called SSGL) is introduced. Firstly, the lost function of SSGL is constructed. The model is improved with the spatial-spectral information of imagery. And then, a Graph Fourier Transform is applied to construct a weighted map for spectral information. After that, a symmetrical normalization Graph Laplacian Matrix is constructed with the aforementioned weighted map. This process constructs a new unmixing model for hyperspectral imagery based on Graph Laplacian. The spatial and spectral information of hyperspectral imagery are jointed together through Graph Laplacian Matrix. Before constructing the Graph Laplacian Matrix, a weight map is calculated uses Cauchy function. Normalization for Graph Laplacian Matrix is acted to eliminate the problem of image scale inconsistency. It makes principal component analysis and standardization of the distance between each node of the weight map, and obtains a more accurate weight map, which further improves the accuracy of unmixing. Secondly, the sparse abundance and endmember constraint is drawn into the unmixing model. Lastly, the iteration termination condition is given to the model. Endmember matrix and abundance matrix are obtained form the iteration process. The result demonstrates that the proposed SSGL unmixing algorithm shows better performance than the other two methods. And, regularization factor actually effects the unmixing result.