Abstract
Aiming at Non-negative Matrix Factorization (NMF)’s problem of initialization and "local minima" in hyperspectral unmixing, a NMF linear unmixing algorithm with spatial correlation constrains (SCNMF) based on Markov Random Field (MRF) was proposed. Firstly, Hyperspectral Signal identification by minimum error (HySime) method was adopted to estimate the number of endmembers, initialized endmember matrix and abundance matrix by Vertex Component Analysis (VCA) and Fully Constrained Least Squares (FCLS) respectively. then established energy function to depict the spatial distribution characteristics of ground objects by MRF model. Finally, spatial correlation constraint based on MRF model and NMF standard objective function were combined in the form of altemating iteration to estimate endmember spectrum and abundance of hyperspectral image. Theoretical analysis and experimental results indicated that, the endmember decomposition precision of SCNMF is 10.6% higher than that of Minimum Volume Constrained NMF (MVC-NMF), 12.3% higher than that of Piecewise Smoothness NMF with Sparseness Constraints(PSNMFSC), 14.1% higher than that of NMF with Alternating Projected Subgradients(APS-NMF); the abundance decomposition precision of SCNMF is 14.4% higher than that of MVC-NMF, 15.9% higher than that of PSNMFSC, 15.3% higher than that of APS-NMF.The proposed SCNMF can remedy NMF's deficiency in describing spatial correlation characteristics, and decrease spatial energy distribution error.
Highlights
Aiming at Non-negative Matrix Factorization (NMF)’s problem of initialization and "local minima" in hyperspectral unmixing, a NMF linear unmixing algorithm with spatial correlation constrains (SCNMF) based on Markov Random Field (MRF) was proposed
Du[6] proposed a semi supervised NMF algorithm based on Graph regularization(GSNMF), which overcomes the defect of ignoring the local geometric structure of sample data; Liu[7] put forward a new hyperspectral unmixing algorithm, by using training data to construct structured dictionary, which introduced space correlation constraints and spatial information of training data; Chen[8] used a priori probability density function to MATEC Web of Conferences 232, 02003 (2018)
Dobrushin[10] pointed out that if the NMF unmixing algorithm does not consider the similarity among adjacent ground objects, and ignores the spatial correlation feature of endmember distribution, other types of endmember or noise will have more interference on endmember’s spatial distribution in unmixing results, which may result in bigger space energy
Summary
"Mixed pixel" is one of the key questions that affect the precision of Hyperspectral Remote Sensing Application. Its formula is similar to the linear spectral mixture model, which makes NMF based unmixing algorithm the hot spot of linear hyperspectral unmixing study Because of problems such as initialization and“local minima”caused by non-convexity, the unmixing effect of standard NMF is unsatisfactory, and numbers of NMF extension algorithms for hyperspectral unmixing emerge. These algorithms can reduce the solution space, speed up the iteration or improve the accuracy of the mixing, by adding some typical features of hyperspectral images into the standard NMF objective function as constraint terms. It uses NMF to realize unmixing procedure and ensure basic unmixing accuracy, adopts MRF model to depict the spatial correlation feature of hyperspectral image, rectifies unmixing error of NMF’s standard objective function, and further improves unmixing accuracy
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