Research On Sparse Unmixing Algorithms For Hyperspectral Remote Sensing Image

Hyperspectral unmixing aims at finding out pure spectral signatures(called endmembers)in a mixed spectral pixel as well as the proportion of each endmember(called abundance),which is an important technology in hyperspectral image processing.It provides favorable basis for more accurate classification,target detection,and other applications.The sparse regression-based methods amount to finding the optimal subset of signatures in a spectral library that can best model each mixed pixel in the scene.This kind of unmixing technology has drawn more and more attention due to the avoidance of endmember estimation.However,there are many false endmembers in the estimated endmember set because of noise in the data and the high mutual correlation of spectral library.Therefore,the accuracy of sparse unmixing is reduced.Regarding to the existing problems in hyperspectral sparse unmixing,several novel methods have been proposed.Moreover,these proposed algorithms are analyzed and validated from the theoretical and experimental views.The main work and achievements of the paper are given as follows.1.The abundance sparse unmixing error is first defined by calculating the difference between the estimated abundance of noisy data and the desired abundance of original data.Since the abundance sparse unmixing error is generated during the process of sparse unmixing,it will affect the accuracy of hyperspectral sparse unmixing.To improve the accuracy of hyperspectral sparse unmixing,we coupled collaborative sparse unmixing and abundance sparse unmixing error reduction together in a unified framework,in which the latter is implemented by a centralized constraint.As such,the estimated abundance will approach the desired abundance of original data.Because the desired abundance is unavailable,the nonlocal spatial redundancy is exploited to yield a good approximation of it,which is implemented in an iterative manner such that the reconstructed hyperspectral data after each iteration contain less noise than that in the previous iterations.and can benefit the patch searching and the approximation quality.The proposed method improves the accuracy and efficiency of estimated abundance.2.Another limitation of sparse unmixing is that the number of the estimated endmembers is more than the true one.This is mainly because that the sparsity constraint of l1 norm or l2,1 norm is not enough in the existing sparse unmixing methods.Meanwhile,these methods also ignore the sparsity of the abundance distribution of each material.To obtain more accurate results,double reweighted l1 norm sparse unmixing framework is proposed to enhance the sparsity of the fractional abundance.According to the fact that the number of endmembers is sparse compared with the spectral library,one weight aims to enhance the sparsity of column of the fractional abundance by suppressing the rows with small norm and encouraging the rows with big norm.Whereas the other weight is to promote the sparsity along the abundance vector corresponding to each endmember by suppressing the abundances with small value and encouraging the abundances with big value.Furthermore,in view of the importance of taking the spatial information into account for sparse unmixing,a TV-based regularization is further incorporated for encouraging spatial homogeneity while preserving discontinuities.Smoothness constraint and the double reweighted l1 norm improve the accuracy of the hyperspectral unmixing.3.A novel sparse unmixing model based on spatial-spectral characteristic is proposed.Three-dimensional characteristic of the hyperspectral data is fully exploited to present a spatial-spectral similarity-based sparse unmixing model.Specifically,each spectral pixel together with its neighboring pixels is combined to form a cube,whose spectral similarities are utilized to construct the similarity weights.On the one hand,these weights are integrated with the observed data to suppress the noise.On the other hand,they represent different contributions of different pixels to the current pixel during unmixing process.According to the manifold structure of the hyperpsectral data,the similarity of pixels will lead to that of abundances.Thus,the abundance of the current pixel can be approximated by the weighted average of its neighboring pixels' abundances.Furthermore,the proposed model is incorporated with the reweighted l1 sparse constraint to improve the sparsity of the estimated abundance and the validity of sparse unmixing.Nonnegative matrix factorization(NMF)decomposes the hyperspectral data into two nonnegative matrices.This property exactly guarantees the nonnegativity constraint(ANC)of endmembers and abundances such that NMF has been widely applied into hyperspectral unmixing.Due to the nonconvexity of the objective function,the corresponding solutions will exist in the local minima.Presently,the NMF-based unmixing methodology mainly focuses on the constraints of endmembers and abundances,but ignores the influence of the initialization.Here,a new initialization method is proposed to improve the accuracy of NMF for hyperspectral unmixing.As far as NMF-based hyperspectral unmixing is concerned,the initialization of endmembers has an important influence on the unmixing results.As we know,the existing unmixing methods include random initialization and vertex component analysis(VCA).In general,the latter performs better than the former.However,VCA requires the existence of pure pixels associated with each endmember,which is difficult to be satisfied in many scenarios.As such,the initialized endmembers by VCA may be different from the true ones,leading to the reduction of the unmixing accuracy.Since the endmembers obtained by sparse unmixing methods include some true endmembers,the change of nuclear norm of sparse abundance matrix is utilized to judge the underlying true endmembers.Specifically,when a row of abundance matrix is deleted,a relatively large change of nuclear norm means the large possibility of a true endmember.Otherwise,the corresponding endmember is impossible to be a true one.Then,we compare the endmembers obtained by norm change(NC)with those extracted from the observed HSI by VCA through quantitatively evaluating the spectral angle.The initial endmembers are obtained by replacing some extracted endmembers obtained by VCA with the estimated ones by NC when the spectral angles are smaller than a given threshold.The obtained endmember initialization will benefit hyperspectral unmixing.