Evolutionary Multiobjective Optimization Based Hyperspectral Image Unmixing

With the rapid development of aerospace and spectral imaging technology,hyperspectral im-age has been increasingly available.It has been widely used in object classification,detec-tion and recognition tasks,and made a series of achievements in food safety,environmental monitoring,agricultural and forestry resources assessment,medical diagnosis and other ap-plication fields because it can provide both the spatial and spectral information of the ground objects.However,due to the limited resolution and the complex as well as diverse distri-bution of the ground features,pixels in hyperspectral image are usually mixtures of more than one distinct substances.In order to get more insight into the ground objects,spectral unmixing is in great demand to decompose the mixed spectra into a certain number of pure spectral signatures(endmembers)and a set of their corresponding fractions(abundances).Hyperspectral unmixing generally needs to optimize some regularization terms inspired by prior knowledge besides the unmixing accuracy,so it's essentially a multiobjective opti-mization problem.Conventional optimization methods generally need to combine multiple objectives into one primarily with regularization parameters,thus trapped in the problem of“decision ahead of solution”,i.e.,presetting the regularization parameters by judging and weighing the multiple objectives before solving the problem.In addition,they generally have a high demand for the analytic properties(e.g.,convexity and differentiability,etc.)of the constructed regularization terms,thus weakening their ability in pursuing the prior knowledge.In contrast,multiobjective optimization method can obtain a set of nondomi-nated solutions using population based evolutionary algorithms without introducing regular-ization parameters,which is one kind of“decision after solution”method.Decision makers can select or synthesize a final solution from the nondominated solutions according to their application needs.This dissertation focuses on developing the evolutionary multiobjective optimization meth-ods for hyperspectral unmxing.Based on the external spectral library and the idea of self-dictionary,the linear,bilinear and nonlinear mixing problems are gradually formulated as multiobjective sparse unmixing problems,which are well solved by proposing a series of population based evolutionary algorithms within the multiobjective evolutionary algorithm based on decomposition(MOEA/D)framework.The contents of this dissertation are sum-marized as follows:(1)A memetic algorithm is proposed for multiobjective sparse nonnegative matrix factoriza-tion.Nonnegative matrix factorization can obtain physically interpretable part-based sparse representation for a given data while implementing dimensional reduction nonlinearly.To further explore the intrinsic structure of the given data under different sparsity,we refor-mulate the nonnegative matrix factorization problem as a multiobjective sparse optimization problem,and propose a memetic algorithm within the MOEA/D framework to search the nondominated solutions.In the memetic algorithm,besides the population based global search,an individual based masked projected gradient local search operator is specially de-signed.The results of comparative experiments indicate that the proposed method can obtain better intrinsic structures of the given data with different sparsity and sparse representations with regard to these intrinsic structures while maintaining high factorization accuracy.(2)A two-phase multiobjective sparse unmixing approach is proposed for the linear mixing hyperspectral image based on the external spectral library.In the first phase,the unmix-ing residuals and the number of endmembers are simultaneously optimized,and a discrete variable optimization algorithm within the MOEA/D framework is proposed to search the nondominated solutions,the Pareto front of which exhibits distinct knee regions in the ex-periments.In addition,the endmembers identified by the solution in the knee region are generally consistent with the real endmembers.Therefore,the knee point search algorithms can be applied to determine the estimated endmembers.In the second phase,the unmixing residuals and the total variation term are simultaneously optimized based on the estimat-ed endmembers,and a memetic algorithm within the MOEA/D framework is proposed to search the nondominated solutions.In the memetic algorithm,the multiplicative update rule in the nonnegative matrix factorization zone is applied as a local search operator.Finally,the abundances are selected from the nondominated solutions according to the application needs.The results of comparative experiments indicate that the proposed method achieves excellent performance in estimating the endmembers as well as the abundances.(3)An improved two-phase multiobjective sparse unmixing approach is proposed by ex-ploiting more spectral and spatial information of the hyperspectral image.To facilitate the identification of endmembers of high accuracy under heavy noise and the estimation of abun-dances as a whole,in the endmember estimation phase,a composite spectral similarity mea-sure constructed by fusing the spectral correlation angle and the Euclidean distance is used to improve the endmember estimation performance under heavy noise because it consid-ers both the shape and amplitude discrepancy between the reconstructed and real spectra.In the abundance estimation process,an_2,?norm based residual objective is constructed and pixel-targeted genetic operators are specially designed,which facilitate the estimation of abundances as a whole.The results of comparative experiments indicate that the perfor-mance of the proposed method in both phases is improved under heavy noise,and the time complexity is also greatly reduced.(4)A multiobjective endmember identification approach is proposed within the bilinear mix-ing paradigm.In contrast to the linear mixing model,the bilinear mixing model is more suitable to describe the mixing process including nonnegligible secondary scattering.How-ever,most bilinear unmixing methods construct the possible secondary scattering using the known endmembers,and mainly focus on estimating their abundances.If the endmembers are inaccurately initialized,the estimated abundances would also be inaccurate.To settle this problem,a multiobjective endmember identification model is constructed by regarding the secondary scattering as a virtual endmember.Under some intuitive constraints,the de-cision space of the problem is greatly reduced.Coupled with the specially designed genetic operators for the virtual endmembers,the efficiency of the algorithm is significantly im-proved.The results of comparative experiments indicate that the proposed method obtains high accuracy in estimating endmembers with almost no extra time cost.(5)A data-driven multiobjective endmember extraction method is proposed for nonlinear mixture data by assuming that the distribution of data conforms to a nonlinear manifold and the endmembers corresponding to its extreme points span the maximum nonlinear simplex along the manifold in the same dimension.By introducing the Cayley-Menger determinant,the geodesic distance between vertices can be used to calculate the spanned nonlinear sim-plex.Multiobjective optimization method can be used to search the boundary points of the manifold and obtain a set of maximum volume simplexes corresponding to different num-bers of vertices.The final endmembers can be obtained according to the volume's change of the simplexes and the related priori knowledge.To improve the efficiency and robustness of the method,a boundary point detection method is proposed to reduce the search space,and the multiple regression technique is applied locally to remove the noise in data.The results of comparative experiments indicate that the proposed method obtains high accuracy in estimating endmembers for the nonlinear mixture data.