Sparsity Constrained Graph Regularized NMF for Spectral Unmixing of Hyperspectral Data
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RESEARCH ARTICLE
Sparsity Constrained Graph Regularized NMF for Spectral Unmixing of Hyperspectral Data Roozbeh Rajabi & Hassan Ghassemian
Received: 17 February 2014 / Accepted: 31 July 2014 # Indian Society of Remote Sensing 2014
Abstract Hyperspectral images contain mixed pixels due to low spatial resolution of hyperspectral sensors. Mixed pixels are pixels containing more than one distinct material called endmembers. The presence percentages of endmembers in mixed pixels are called abundance fractions. Spectral unmixing problem refers to decomposing these pixels into a set of endmembers and abundance fractions. Due to non negativity constraint on abundance fractions, non negative matrix factorization methods (NMF) have been widely used for solving spectral unmixing problem. In this paper we have used graph regularized NMF (GNMF) method combined with sparseness constraint to decompose mixed pixels in hyperspectral imagery. This method preserves the geometrical structure of data while representing it in low dimensional space. Adaptive regularization parameter based on temperature schedule in simulated annealing method also has been used in this paper for the sparseness term. Proposed algorithm is applied on synthetic and real datasets. Synthetic data is generated based on endmembers from USGS spectral library. AVIRIS Cuprite dataset is used as real dataset for evaluation of proposed method. Results are quantified based on spectral angle distance (SAD) and abundance angle distance (AAD) measures. Results in comparison with other methods show that the proposed method can unmix data more effectively. Specifically for the Cuprite dataset, performance of the proposed method is approximately 10 % better than the VCA and Sparse NMF in terms of root mean square of SAD.
R. Rajabi (*) : H. Ghassemian ECE Department, Tarbiat Modares University, Tehran 14115-111, Iran e-mail: [email protected] H. Ghassemian e-mail: [email protected]
Keywords Hyperspectral imaging . Spectral unmixing . Nonnegative matrix factorization (NMF) . Graph regularization . Sparseness constraint
Introduction Mixed pixels appear in hyperspectral images due to low spatial resolution of hyperspectral sensors (Keshava 2003). Fig. 1 illustrates the basic concept of mixed pixels in hyperspectral images (Rajabi and Ghassemian 2011). Pure pixel refers to a pixel that is composed of only one distinct material and mixed pixel refers to a pixel containing more than one distinct material. Spectral unmixing problem has many applications in hyperspectral data analysis, for example it can be used to classify the hyperspectral data at a finer spatial resolution (Villa et al. 2011), hyperspectral and multispectral image fusion (Bendoumi and Mingyi 2013). Spectral unmixing algorithms decompose a mixed pixel into a set of endmembers and abundance fraction maps (Sanjeevi and Barnsley 2000). Fig. 2 shows a toy example that demonstrates spectral unmixing process. Endmembers are the spectral signatures that are present in the scene and abundance fractions are
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