Hyperspectral Image Unmixing Algorithms Based On Manifold And Robust Estimation

Hyperspectral remote sensing technique is proposed in 1980s,which has enjoyed a rapid development in recent decades.Unlike the classical remote sensing technique,hy-perspectral remote sensing has characteristics like much more bands,narrow interval be-tween adjacent bands,high spectral resolution,large amount of data,large data redundancy,'image-spectrum merging'.Even with significant development of remote sensing technique,there still exists low spatial resolution in hyperspectral images,which results from the limi-tation of existing imaging spectroscopy techniques and complex diversity of ground objects.This gives rise to the phenomenon that a lot of observed pixel spectra is not the spectra from a pure material,but a mixture from different materials,which is called mixed pixel.But in different mixed pixels,the composition of each substance can vary widely and even mul-tiple spectra have mutual influence and multiple scattering.As a result,people are unable to recognize the spectral information of pure endmember they need,and cannot understand the structure of the ground objects in the region.This naturally generates hyperspectral image unmixing technique,which is used to obtain pure endmember spectra and their abun-dance.But Owing to the model's inaccuracy,observation noise,environmental conditions,end element diversity and so on,Hyperspectral unmixing has been a challenging research field.Non-negative matrix factorization(NMF)has already been a popular hyperspectral im-age unmixing technique.Its main character lies on the fact that non-negative matrix factor-ization requires that all the elements of the decomposed two matrices and the original data matrix are non-negative.At the same time,the hyperspectral unmixing problem can also be regarded as solving a set of basis vectors and the corresponding coefficient matrix from a observed data matrix.Although non-negative matrix factorization has become one of the main hyperspectral unmixing algorithms,there are still several difficulties in non-negative matrix factorization unmixing algorithm.For example,the model is non-convex for both two matrices,and easy to achieve local optimal;the intrinsic geometric structure of pixels is often not considered;the convergence rate of the commonly used iterative algorithm is too slow;the model is unstable and sensitive to noise;and so on.Therefore,to deal with the above problems,we carry out systematic research and dis-cussion,and design a series of optimization algorithms based on the existing unsupervised non-negative matrix factorization mixing algorithm,by integrating with the knowledge of matrix manifold optimization and robust estimation,and so on.The main research work of this paper is as follows:1.Since the common non-negative matrix factorization algorithms seldom consider the inherent structure of the abundance matrix,we propose a L₁-NMF model based on Oblique manifold(L₁-OB NMF).The critical idea of the proposed method is to transform the abundance matrix into a new pattern which locates on the oblique manifold;this opera-tion eliminates the Abundance nonnegativity Constraint(ANC)and the Abundance Sum-to-one Constraint(ASC)and transforms the original conditional constraint problem becomes the unconditional constraint problem.Meanwhile,by reforming L_1/2regularization into L₁on the manifold,the computational complexity can be reduced without damaging its per-formance.Moreover,due to the fast convergence rate of conjugated gradient method,we propose a nonlinear conjugate gradient algorithm on Oblique manifold to implement rapid convergence,and we prove the convergence of the proposed algorithm.Experiments on artificial data set,Jasper data set and Cuprite data set demonstrate the effectiveness of the algorithm.2.Our first study only considers the abundance matrix as a whole,but not consider adequately the internal structure of the abundance matrix.The mutual information between abundance vectors is benificial to keep the inner geometric structure of abundance matrix,which will make the model more discriminative.Thus,based on L₁-OB NMF,we propose a new L₁-OB NMF model based on graph regularization.The core idea of the model is to assume that when the spectra of two pixels are close in the original sample space,they are still close in the abundance space.Moreover,integrating multiplicative iterative rule and nonlinear conjugated gradient method,we propose a fast iterative algorithm to solve the model.Moreover,we prove the convergence of the proposed algorithm.Experiments on artificial data set and Cuprite data set demonstrate the effectiveness of the algorithm.3.Since the L₂objective function in the standard NMF algorithm is sensitive to noise,we propose a modifed-Huber NMF algorithm.The main idea of this algorithm is to replace the least square function with the modified Huber function as the objec-tive function,to give the new model better robustness to noise.In addition,we adopt Hollan&Welsch rule,which multiplies a constant and the median error absolute value to be the tunning parameter;and utilize nonlinear projected conjugated gradient method to get improved half-quadratic optimization algorithm for the solution.These will lead to better unmixing performance and faster convergence rate.Experiments on artificial data set,Samson data set and Cuprite data set demonstrate the effectiveness of the algorithm.