Unmixing Techniques Of Hyperspectral Remote Sensing Image Based On Sparse Regression

Hyperspectral images are acquired using airborne or spaceborne sensor,which record in-formation over hundreds of narrow and contiguous spectral bands（usually in the visible and infrared regions of the electromagnetic spectrum）in the same scene.Taking advantage of the abundant spectral information,hyperspectral images have been widely used to distinguish dif-ferent types of land-cover classes having similar spectral signatures in agriculture,mineralogy,etc.The mixed pixels appear in the observed hyperspectral image data since the low spatial resolution of the sensors does not resolve different materials in one pixel.How to extract and separate the pure spectral signatures from the mixed pixels and determine the corresponding proportions becomes the key issue for the hyperspectral images analysis and its quantification application.Spectral unmixing aims at identifying the pure materials（or endmembers）and simulta-neously estimating corresponding proportions（or abundances）in the（possibly mixed）pixel,and has been extensively explored in the last few decades.With the widespread use of the spectral libraries,the sparse-representation-based approaches have drew much attention.The sparse-regression based techniques assume that the mixed pixels are represented by linear com-binations of a small number of endmembers from a spectral library that is known in advance.In this case,the unmixing becomes a problem of finding the best subset of signatures in the library to represent all the pixels in a given hyperspectral image.The existing sparse-regression based techniques still have some limitations:（i）The sparse unmixing models are solved by the prime alternating direction method of multipliers.However,the computation task of prime alternating direction method of multipliers is heavy and time consuming.（ii）Most of the sparse-regression based techniques focus on the abundance information but ignore the abundance gradient infor-mation,that is,only implement sparsity on the abundance but not on the gradient;（iii）For the unmixing methods that consider the group structure of the spectral library,most of the models treat the pixel individually and do not enforce homogeneity in the abundances of neigh-boring pixels.To solve the above problems,this thesis studies the sparse-regression based techniques.New methods and techniques for unmixing are developed considering or without considering the group structure of the spectral library respectively.While this thesis provides new frameworks or new ideas for follow-up research,it also provides the theoretical foundation and technical support for improving the utilization of hyperspectral remote sensing data.The main work and contributions are summarized as follows:（1）The classic sparse unmixing models are solved by the prime alternating direction method of multipliers.However,the computation task of prime alternating direction method of multipliers is heavy and time consuming.We design a novel dual alternating direction method of multipliers for the classic sparse unmixing models.We also present the global convergence analysis of our algorithm in some special cases.An important aspect of the proposed algorithm framework is that it can be applied to various types of spectral and spatial weighting factors,such as homogeneous neighborhood information,nonlocal similarity,and edge information.As shown in our experiments,the proposed algorithm is more effective than the state-of-the-art algorithms.（2）The total variation has been widely used to promote the spatial homogeneity as well as the smoothness between adjacent pixels.However,the computation task for hyperspectral sparse unmixing with a total variation regularization term is heavy.Besides,the convergence of the primal alternating direction method of multipliers for the hyperspectral sparse unmix-ing with a total variation regularization term has not been explained in details.We design an efficient and convergent dual symmetric Gauss-Seidel alternating direction method of multi-pliers for hyperspectral sparse unmixing with a total variation regularization term.We also present the global convergence and local linear convergence rate analysis for this algorithm.As demonstrated in numerical experiments,our algorithm can obviously improve the efficiency of the unmixing compared with the state-of-the-art algorithm.（3）l₁regularizer has been widely considered as a regularization strategy to exploit the sparsity of the unmixing solution.Further sparsity can be imposed by also using weighting factors.However,most existing strategies focus on the unmixing solution ignoring the gradient information.To account for the gradient information in hyperspectral unmixing,we propose a weighted sparse regression with total variation unmixing model.The proposed model in-corporates gradient information in the sparse regression formulation by means of the weighted total variation regularizer.The model imposes sparsity on both the solution and the gradient to improve the performance of unmixing.A dual symmetric Gauss-Seidel alternating direc-tion method of multipliers is designed to optimize the proposed model.Then,an extended fast projected gradient algorithm was designed to solve the resulting subproblem.The designed algorithm both handles the anisotropic and isotropic weighted total variation.Simulated and real hyperspectral data demonstrate the effectiveness of the proposed framework.（4）The available spectral library organizes spectral signatures in groups.However,most existing strategies do not take full advantage of the inherent properties in the library.We design a convex framework for sparse unmixing that incorporates the group structure of the spectral library.The convex framework includes two kinds of algorithms derived from either the primal or the dual form of the alternating direction method of multipliers.Then,the convergence properties of the convex framework are established.Based on the convex framework,a novel nonconvex framework is developed for unmixing,which provides a new manner to enhance the sparsity of solution.The core of the nonconvex framework is to design a nonconvex penalty function for efficient minimization utilizing the generalized shrinkage mapping.The penalty function can be regarded as a closer approximation of the7)₀norm.Experiments conducted on simulated and real hyperspectral data demonstrate the superiority and effectiveness of the proposed nonconvex framework in improving the unmixing performance and enhancing the sparsity of solution with respect to state-of-the-art techniques.This thesis mainly studies the hyperspectral unmixing techniques based on sparse regres-sion under the linear mixing model.New unmixing schemes are designed considering or with-out considering the group structure of the spectral library respectively.The effectiveness of the proposed scheme is verified by simulated and real hyperspectral remote sensing data.