A Study Of Hyperspectral Unmixing Based On Low-rank Constrained Non-negative Matrix Factorization

Hyperspectral remote sensing imaging is one of the hotspots in the field of field observation.The hyperspectral image contains spectral information of tens to hundreds of bands,which provides a powerful basis for the classification of features and feature recognition.However,the continuous improvement of the spectral resolution of the hyperspectral image affects its spatial resolution,resulting in the widespread existence of mixed pixels in hyperspectral images,that is,a cell containing a mixture of spectra of different objects,and thus greatly affected the classification of objects and the accuracy of ground recognition.Hyperspectral unmixing is an algorithm that divides a mixed pixel into a product of the spectral vector?endmembers?and its corresponding proportion?abundance?,and the use of precision end-extraction and abundance estimation can further improve the use of subsequent classification or sub-pixel information.Therefore,hyperspectral image mixed pixel decomposition is an important research content in hyperspectral technology.Non-negative Matrix Factorization?NMF?is an algorithm that decomposes a nonnegative matrix into two nonnegative matrix product forms.It is consistent with the hyperspectral linear mixed model,which reflects the intuitionistic characteristics of the whole part of the data perception.However,NMF is a ill problem,and it can often fall into the local optimal solution when applied directly to hyperspectral unmixing.Aiming at this problem,this paper designs the hyperspectral unmixing algorithm based on low-rank constrained non-negative matrix factorization.Specific work is as follows:?1?A hyperspectral data unmixing method based on local low-rank constrained NMF?LLrNMF?is designed for the shortcomings of the existing NMF linear unmixing model which does not make full use of the spatial structure information.Firstly,the hyperspectral image is divided into superpixel segmentation,and the low-rank constraint is added to the non-negative matrix unmixing model.For the low rank constraint can be regarded as a combination of sparse constraint and spatial structure information,this method can keep the spatial structure information when the image is under the sparse constraint.Experiments were carried out on two groups of synthetic hyperspectral data and two sets of real hyperspectral images.The accuracy of the endmembers extraction and abundance estimation was compared and the influence of the algorithm parameters on the results was discussed.The results show that the proposed method is superior to VCA,L_1/2NMF,GLNMF?Graphed NMF?,WNMF and other advanced methods in terms of algorithm convergence,numerical indicators SAD and RMSE,algorithm stability and visual effect.?2?A hyperspectral unmixing algorithm based on low-rank constrained NMF?GBM-Lr NMF?is proposed to overcome the limitation of needing to use the information of supervisory.This method is based on the generalized bilinear model?GBM?.It is not necessary to assume that the end mappings are known and the gradient matrix is used to optimize the end matrix,abundance matrix and nonlinear abundance matrix.Experiments were carried out on synthetic hyperspectral data and real hyperspectral images.Compared with VCA,NMF,GBM-semiNMF and other methods,the results show that the objective function of this method converges faster,and it is superior to VCA,NMF,GBM-semiNMF and other advanced methods in numerical indicators SAD and RMSE,and visual effect.?3?A robust nonnegative matrix unmixing algorithm based on low-rank constraint is proposed for the characteristics of non-Gaussian impulsive noise in origial hyperspectral data.Based on the noise model,a robust nonnegative matrix unmixing algorithm based on manifold regularization?GRNMF?is designed on the basis of the above work.In the robust nonnegative matrix unmixing model,the low-rank constraint of endmembers and abundance is constrained by the robust model,and a new space-manifolds of the pixels selected by using the space-spectrum information is added to the robust NMF model.The experimental results are carried out in two groups of artificial hyperspectral data and two sets of real hyperspectral images,and the influence of algorithm parameters on the results is discussed.The experimental results show that this method is superior to VCA in the evaluation index SAD and RMSE,the stability of the algorithm and the visual effect.The experimental results show that the proposed method is superior to VCA,GLNMF,SLNMF,SRNMF and other advanced methods in terms of numerical indicators SAD and RMSE,algorithm stability and visual effect.This work was supported by the National Basic Research Program of China?973Program?under Grant no.2013CB329402,National Science Foundation of China under Grant no.91438103,Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant no.20120203110005.